Edit Profile Titi, Edriss Saleh Compute Distance To: Compute Author ID: titi.edriss-saleh Published as: Titi, E. S.; Titi, Edriss; Titi, Edriss S.; Titi, Edriss Saleh External Links: MGP · Wikidata Documents Indexed: 220 Publications since 1985, including 1 Book Biographic References: 1 Publication all top 5 Co-Authors 5 single-authored 22 Cao, Chongsheng 18 Jolly, Michael S. 15 Foiaş, Ciprian Ilie 14 Constantin, Peter 13 Olson, Eric J. 12 Li, Jinkai 11 Kevrekidis, Ioannis George 11 Lunasin, Evelyn M. 10 Bardos, Claude Williams 10 Farhat, Aseel 9 Guo, Yanqiu 9 Jones, Don A. 7 Holm, Darryl D. 7 Ilyin, Alexei A. 6 Oliver, Marcel 5 Cao, Yanping 5 García-Archilla, Bosco 5 Levant, Boris 5 Linshiz, Jasmine S. 5 Novo, Julia 5 Nussenzveig Lopes, Helena Judith 4 Kalantarov, Varga K. 4 Larios, Adam 4 Lopes Filho, Milton da Costa 4 Martinez, Vincent R. 4 Mondaini, Cecilia F. 4 Wynne, Shannon 3 Artstein, Zvi 3 Chen, Shiyi 3 Doelman, Arjen 3 Doering, Charles R. 3 Duan, Jinqiao 3 Gibbon, John D. 3 Liu, Xin 3 Ly, Hung Van 3 Niu, Dongjuan 3 Rammaha, Mohammad A. 3 Sadigov, Tural 3 Seregin, Gregory A. 3 Wiedemann, Emil 2 Azouani, Abderrahim 2 Bessaih, Hakima 2 Biswas, Animikh 2 Chepyzhov, Vladimir V. 2 Cockburn, Bernardo 2 Friedlander, Susan Jean 2 Giga, Yoshikazu 2 Hieber, Matthias 2 Hittmeir, Sabine 2 Holmes, Philip J. 2 Ibrahim, Slim 2 Klein, Rupert 2 Kravchenko, Rostyslav V. 2 Kukavica, Igor 2 Kupferman, Raz 2 Kurien, Susan 2 Levermore, C. David 2 Lin, Quyuan 2 Margolin, Len G. 2 Mazzucato, Anna L. 2 Musslimani, Ziad H. 2 Ramos, Fabio Tozeto 2 Slemrod, Marshall 2 Trabelsi, Saber 2 Vishik, Marko Iosifovich 2 Xin, Zhouping 2 Zang, Aibin 2 Ziane, Mohammed 1 Abu-Saris, Raghib M. 1 Albanez, Débora A. F. 1 Altaf, M. Umer 1 Aubry, Nadine 1 Babin, Anatoli V. 1 Barcilon, Victor 1 Bellout, Hamid 1 Benachour, Said 1 Bennis, Anne-Claire 1 Benzi, Roberto 1 Biferale, Luca 1 Bishop, Alan Reginald 1 Bloch, Anthony M. 1 Bollerman, Peter 1 Brown, Harry S. 1 Cao, Yu 1 Castillo-Chavez, Carlos 1 Celik, Emine 1 Chernyshenko, Sergei I. 1 Cheskidov, Alexey 1 Chung, Yunro 1 Collet, Pierre 1 Devulder, Christophe 1 E, Weinan 1 Elaydi, Saber Nasr 1 Ettinger, Boris 1 Fefferman, Charles Louis 1 Ferrari, Andrew B. 1 Flandoli, Franco 1 Frisch, Uriel 1 Gebrael, T. 1 Gerard, Patrick ...and 65 more Co-Authors all top 5 Serials 19 Nonlinearity 11 Journal of Differential Equations 11 Physica D 11 Journal of Nonlinear Science 9 Communications in Mathematical Physics 8 Journal of Mathematical Physics 8 Journal of Dynamics and Differential Equations 7 Archive for Rational Mechanics and Analysis 7 SIAM Journal on Mathematical Analysis 6 Indiana University Mathematics Journal 6 SIAM Journal on Numerical Analysis 6 Journal of Mathematical Fluid Mechanics 5 Communications on Pure and Applied Mathematics 5 Journal of Statistical Physics 5 Numerical Functional Analysis and Optimization 5 Discrete and Continuous Dynamical Systems 5 Communications in Mathematical Sciences 5 Oberwolfach Reports 4 Journal of Mathematical Analysis and Applications 4 Comptes Rendus de l’Académie des Sciences. Série I 3 Mathematics of Computation 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 SIAM Journal on Applied Dynamical Systems 2 Russian Mathematical Surveys 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Theoretical and Computational Fluid Dynamics 2 Journal of Functional Analysis 2 Chinese Annals of Mathematics. Series B 2 Communications in Partial Differential Equations 2 Physics of Fluids 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Discrete and Continuous Dynamical Systems. Series B 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Physics A: Mathematical and Theoretical 2 Evolution Equations and Control Theory 1 IMA Journal of Numerical Analysis 1 Physics Letters. A 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Asymptotic Analysis 1 Journal of Scientific Computing 1 European Journal of Applied Mathematics 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Scientific Computing 1 Calculus of Variations and Partial Differential Equations 1 Sbornik: Mathematics 1 Annals of Mathematics. Second Series 1 Computational Geosciences 1 Physical Review Letters 1 Journal of Turbulence 1 Nonlinear Analysis. Real World Applications 1 Advanced Nonlinear Studies 1 Physical Review E. Third Series 1 Communications in Information and Systems 1 Multiscale Modeling & Simulation 1 Dynamics of Partial Differential Equations 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Communications in Computational Physics 1 Discrete and Continuous Dynamical Systems. Series S 1 Journal of Geometric Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Pure and Applied Functional Analysis 1 Mathematics of Climate and Weather Forecasting all top 5 Fields 192 Partial differential equations (35-XX) 141 Fluid mechanics (76-XX) 46 Dynamical systems and ergodic theory (37-XX) 37 Numerical analysis (65-XX) 34 Geophysics (86-XX) 21 Ordinary differential equations (34-XX) 20 Systems theory; control (93-XX) 6 General and overarching topics; collections (00-XX) 6 Operator theory (47-XX) 5 Probability theory and stochastic processes (60-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Quantum theory (81-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Biology and other natural sciences (92-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 199 Publications have been cited 4,984 times in 2,220 Documents Cited by ▼ Year ▼ The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. Zbl 0995.35051Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 172 2002 The Navier-Stokes-alpha model of fluid turbulence. Zbl 1037.76022Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. 158 2001 Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Zbl 0818.35085Constantin, Peter; E, Weinan; Titi, Edriss S. 142 1994 Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Zbl 1151.35074Cao, Chongsheng; Titi, Edriss S. 136 2007 Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Zbl 1042.76525Chen, Shiyi; Foias, Ciprian; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 131 1998 On a Leray-\(\alpha\) model of turbulence. Zbl 1145.76386Cheskidov, Alexey; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. 123 2005 Regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1159.35053Cao, Chongsheng; Titi, Edriss S. 103 2008 A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Zbl 1147.76357Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 98 1999 Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models. Zbl 1127.35034Cao, Yanping; Lunasin, Evelyn M.; Titi, Edriss S. 91 2006 Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. Zbl 1256.35051Cao, Chongsheng; Titi, Edriss S. 89 2011 The Camassa-Holm equations and turbulence. Zbl 1194.76069Chen, S.; Foias, C.; Holm, D. D.; Olson, E.; Titi, E. S.; Wynne, S. 85 1999 Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations. Zbl 0692.35053Foias, Ciprian; Sell, George R.; Titi, Edriss S. 84 1989 Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations. Zbl 0704.58030Jolly, M. S.; Kevrekidis, I. G.; Titi, E. S. 82 1990 Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations. Zbl 0796.35128Jones, Don A.; Titi, Edriss S. 73 1993 Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion. Zbl 1284.35343Larios, Adam; Lunasin, Evelyn; Titi, Edriss S. 71 2013 Determining nodes, finite differences schemes and inertial manifolds. Zbl 0714.34078Foias, Ciprian; Titi, Edriss S. 68 1991 Global attractors and determining modes for the 3D Navier-Stokes-Voight equations. Zbl 1178.37112Kalantarov, Varga K.; Titi, Edriss S. 66 2009 On approximate inertial manifolds to the Navier-Stokes equations. Zbl 0723.35063Titi, Edriss S. 63 1990 Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in \(\mathbb{R}^n\). Zbl 0960.35081Oliver, Marcel; Titi, Edriss S. 62 2000 Global stability of large solutions to the 3D Navier-Stokes equations. Zbl 0795.35082Ponce, G.; Racke, R.; Sideris, T. C.; Titi, E. S. 58 1994 Gevrey regularity for nonlinear analytic parabolic equations. Zbl 0907.35061Ferrari, Andrew B.; Titi, Edriss S. 57 1998 Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models. Zbl 1062.35080Cao, Chongsheng; Holm, Darryl D.; Titi, Edriss S. 54 2004 Global well-posedness and finite-dimensional global attractor for a 3-D planetary geostrophic viscous model. Zbl 1035.37043Cao, Chongsheng; Titi, Edriss S. 54 2003 A modified-Leray-\(\alpha\) subgrid scale model of turbulence. Zbl 1106.35050Ilyin, Alexei A.; Lunasin, Evelyn M.; Titi, Edriss S. 53 2006 Analytical study of certain magnetohydrodynamic-\(\alpha\) models. Zbl 1144.81378Linshiz, Jasmine S.; Titi, Edriss S. 52 2007 Euler equations for incompressible ideal fluids. Zbl 1139.76010Bardos, C.; Titi, E. S. 52 2007 Preserving symmetries in the proper orthogonal decomposition. Zbl 0774.65084Aubry, Nadine; Lian, Wen-Yu; Titi, Edriss S. 47 1993 Determining finite volume elements for the 2D Navier-Stokes equations. Zbl 0778.35084Jones, Don A.; Titi, Edriss S. 47 1992 The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom. Zbl 0928.35120Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S. 46 1999 Continuous data assimilation using general interpolant observables. Zbl 1291.35168Azouani, Abderrahim; Olson, Eric; Titi, Edriss S. 42 2014 Invariant helical subspaces for the Navier-Stokes equations. Zbl 0708.76044Mahalov, A.; Titi, E. S.; Leibovich, S. 42 1990 Global existence theory for a generalized Ginzburg-Landau equation. Zbl 0783.35070Duan, Jinqiao; Holmes, Philip; Titi, Edriss S. 41 1992 Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. Zbl 0808.35133Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip 39 1993 Postprocessing the Galerkin method: A novel approach to approximate inertial manifolds. Zbl 0914.65105García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. 38 1998 On the regularization mechanism for the periodic Korteweg-de Vries equation. Zbl 1284.35365Babin, Anatoli V.; Ilyin, Alexei A.; Titi, Edriss S. 37 2011 On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models. Zbl 1202.35172Larios, Adam; Titi, Edriss S. 37 2010 Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. Zbl 1023.76513Doering, Charles R.; Titi, Edriss S. 37 1995 Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Zbl 0866.35091Cockburn, Bernardo; Jones, Don A.; Titi, Edriss S. 36 1997 Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Zbl 1336.35297Li, Jinkai; Titi, Edriss S. 34 2016 Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model. Zbl 1339.35246Markowich, Peter A.; Titi, Edriss S.; Trabelsi, Saber 33 2016 Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations. Zbl 1177.35152Kalantarov, Varga K.; Levant, Boris; Titi, Edriss S. 33 2009 Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Zbl 1317.35262Cao, Chongsheng; Ibrahim, Slim; Nakanishi, Kenji; Titi, Edriss S. 32 2015 Continuous data assimilation with stochastically noisy data. Zbl 1308.35161Bessaih, Hakima; Olson, Eric; Titi, Edriss S. 32 2015 Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations. Zbl 1302.76048Hayden, Kevin; Olson, Eric; Titi, Edriss S. 32 2011 An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations. Zbl 0930.76063García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. 32 1999 Continuous data assimilation for the 2D Bénard convection through velocity measurements alone. Zbl 1364.76053Farhat, Aseel; Jolly, Michael S.; Titi, Edriss S. 31 2015 Feedback control of nonlinear dissipative systems by finite determining parameters – a reaction-diffusion paradigm. Zbl 1304.35715Azouani, Abderrahim; Titi, Edriss S. 31 2014 Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models. Zbl 1110.76011Olson, Eric; Titi, Edriss S. 31 2007 On the number of determining nodes for the 2D Navier-Stokes equations. Zbl 0773.35050Jones, Don A.; Titi, Edriss S. 31 1992 Analysis of a mixture model of tumor growth. Zbl 1292.35153Lowengrub, John; Titi, Edriss; Zhao, Kun 30 2013 Determining modes for continuous data assimilation in 2D turbulence. Zbl 1137.76402Olson, Eric; Titi, Edriss S. 29 2003 On the convergence of solutions of the Leray-\(\alpha\) model to the trajectory attractor of the 3D Navier-Stokes system. Zbl 1146.35071Chepyzhov, Vladimir V.; Titi, Edriss S.; Vishik, Mark I. 28 2007 Global well-posedness for models of shallow water in a basin with a varying bottom. Zbl 0953.76011Levermore, C. David; Oliver, Marcel; Titi, Edriss S. 28 1996 A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations. Zbl 1373.76027Gesho, Masakazu; Olson, Eric; Titi, Edriss S. 27 2016 Continuous data assimilation for the three-dimensional Navier-Stokes-\(\alpha\) model. Zbl 1344.35078Albanez, Débora A. F.; Nussenzveig Lopes, Helena J.; Titi, Edriss S. 27 2016 On the rate of convergence of the nonlinear Galerkin methods. Zbl 0783.65053Devulder, Christophe; Marion, Martine; Titi, Edriss S. 27 1993 Dissipativity of numerical schemes. Zbl 0734.65080Foias, C.; Jolly, M. S.; Kevrekidis, I. G.; Titi, E. S. 27 1991 Existence of solutions to the Stommel-Charney model of the gulf stream. Zbl 0679.76108Barcilon, V.; Constantin, P.; Titi, E. S. 27 1988 Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems. Zbl 1123.35043Constantin, P.; Fefferman, C.; Titi, E. S.; Zarnescu, A. 26 2007 Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity. Zbl 1305.35113Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 25 2014 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 24 2016 Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field. Zbl 1334.35202Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 24 2016 Stability of two-dimensional viscous incompressible flows under three-dimensional perturbations and inviscid symmetry breaking. Zbl 1291.35207Bardos, C.; Lopes Filho, M. C.; Niu, Dongjuan; Nussenzveig Lopes, H. J.; Titi, E. S. 24 2013 Global well-posedness of the \(3D\) primitive equations with partial vertical turbulence mixing heat diffusion. Zbl 1267.35157Cao, Chongsheng; Titi, Edriss S. 24 2012 On the domain of analyticity for solutions of second order analytic nonlinear differential equations. Zbl 1001.34003Oliver, Marcel; Titi, Edriss S. 24 2001 Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrödinger equation. Zbl 0912.35144Oliver, Marcel; Titi, Edriss S. 24 1998 Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation. Zbl 0792.35096Doelman, Arjen; Titi, Edriss S. 24 1993 Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. Zbl 1300.35089Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 23 2014 Loss of smoothness and energy conserving rough weak solutions for the \(3d\) Euler equations. Zbl 1191.76057Bardos, Claude; Titi, E. S. 23 2010 Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations. Zbl 1084.35058Ilyin, A. A.; Miranville, A.; Titi, E. S. 23 2004 Distributed and boundary control of the viscous Burgers’ equation. Zbl 0876.93045Ly, Hung V.; Mease, Kenneth D.; Titi, Edriss S. 23 1997 Onsager’s conjecture for the incompressible Euler equations in bounded domains. Zbl 1390.35241Bardos, Claude; Titi, Edriss S. 22 2018 Downscaling the 2D Bénard convection equations using continuous data assimilation. Zbl 1383.65088Altaf, M. U.; Titi, E. S.; Gebrael, T.; Knio, O. M.; Zhao, L.; McCabe, M. F.; Hoteit, I. 22 2017 On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model. Zbl 1188.35135Levant, Boris; Ramos, Fabio; Titi, Edriss S. 22 2010 Finite determining parameters feedback control for distributed nonlinear dissipative systems – a computational study. Zbl 1375.35256Lunasin, Evelyn; Titi, Edriss S. 21 2017 Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Zbl 1351.35125Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 21 2016 Global well-posedness of strong solutions to a tropical climate model. Zbl 1339.35325Titi, Edriss; Li, Jinkai 21 2016 On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations. Zbl 1375.35348Linshiz, Jasmine S.; Titi, Edriss S. 21 2010 The postprocessing Galerkin and nonlinear Galerkin methods – a truncation analysis point of view. Zbl 1130.65314Margolin, Len G.; Titi, Edriss S.; Wynne, Shannon 21 2003 Postprocessing the Galerkin method: The finite-element case. Zbl 0952.65078García-Archilla, Bosco; Titi, Edriss S. 21 2000 A remark on quasi-stationary approximate inertial manifolds for the Navier-Stokes equations. Zbl 0808.35102Jones, D. A.; Titi, E. S. 21 1994 On a criterion for locating stable stationary solutions to the Navier- Stokes equations. Zbl 0642.76031Titi, Edriss Saleh 21 1987 A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Zbl 1144.81329Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S. 20 2007 Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations. Zbl 1106.35049Ilyin, A. A.; Titi, E. S. 20 2006 Asymptotic states of a Smoluchowski equation. Zbl 1086.76003Constantin, P.; Kevrekidis, I. G.; Titi, E. S. 20 2004 Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements. Zbl 1334.35230Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 19 2016 Slow observables of singularly perturbed differential equations. Zbl 1140.34025Artstein, Zvi; Kevrekidis, Ioannis G.; Slemrod, Marshall; Titi, Edriss S. 19 2007 Analytic study of shell models of turbulence. Zbl 1113.34044Constantin, Peter; Levant, Boris; Titi, Edriss S. 19 2006 Continuous data assimilation for a 2D Bénard convection system through horizontal velocity measurements alone. Zbl 1365.35108Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 18 2017 On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in \(\mathbb{R}^2\). Zbl 1332.76013Li, Jinkai; Titi, Edriss S.; Xin, Zhouping 18 2016 On convergence of trajectory attractors of the 3D Navier-Stokes-\(\alpha \) model as \(\alpha \) approaches 0. Zbl 1137.37037Vishik, M. I.; Titi, E. S.; Chepyzhov, V. V. 18 2007 On the effectiveness of the approximate inertial manifold – a computational study. Zbl 0838.76066Jones, Don A.; Margolin, Len G.; Titi, Edriss S. 18 1995 A determining form for the two-dimensional Navier-Stokes equations: the Fourier modes case. Zbl 1426.76103Foias, Ciprian; Jolly, Michael S.; Kravchenko, Rostyslav; Titi, Edriss S. 17 2012 Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit. Zbl 1387.35462Ramos, Fabio; Titi, Edriss S. 17 2010 Remarks on a Smoluchowski equation. Zbl 1138.35336Constantin, Peter; Kevrekidis, Ioannis; Titi, Edriss S. 17 2004 Attractors for the two-dimensional Navier–Stokes-\({\alpha}\) model: an \({\alpha}\)-dependence study. Zbl 1039.35078Ilyin, A. A.; Titi, E. S. 17 2003 Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg-Landau equation. Zbl 0849.35014Takáč, P.; Bollerman, P.; Doelman, A.; van Harten, A.; Titi, E. S. 17 1996 On the evolution of nearly circular vortex patches. Zbl 0673.76025Constantin, P.; Titi, E. S. 17 1988 On the Charney conjecture of data assimilation employing temperature measurements alone: the paradigm of 3D planetary geostrophic model. Zbl 1364.86017Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 16 2016 Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers. Zbl 1364.35277Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Titi, Edriss S.; Zang, Aibin 16 2015 Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the Navier-Stokes equations. Zbl 1448.65157García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. 4 2020 Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent. Zbl 1437.35542Luo, Tianwen; Titi, Edriss S. 2 2020 On the well-posedness of reduced \(3D\) primitive geostrophic adjustment model with weak dissipation. Zbl 1440.35263Cao, Chongsheng; Lin, Quyuan; Titi, Edriss S. 1 2020 Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes. Zbl 1447.35267Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S. 1 2020 Onsager’s conjecture with physical boundaries and an application to the vanishing viscosity limit. Zbl 1420.35203Bardos, Claude; Titi, Edriss S.; Wiedemann, Emil 8 2019 On the extension of Onsager’s conjecture for general conservation laws. Zbl 1420.35202Bardos, Claude; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Titi, Edriss S.; Wiedemann, Emil 5 2019 The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation. Zbl 1412.35224Li, Jinkai; Titi, Edriss S. 5 2019 Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations. Zbl 1420.35181Biswas, Animikh; Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 5 2019 Global existence of weak solutions to the compressible primitive equations of atmospheric dynamics with degenerate viscosities. Zbl 1419.35150Liu, Xin; Titi, Edriss S. 4 2019 Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation. Zbl 1427.35204Jolly, Michael S.; Martinez, Vincent R.; Olson, Eric J.; Titi, Edriss S. 3 2019 Spectral filtering of interpolant observables for a discrete-in-time downscaling data assimilation algorithm. Zbl 1428.35276Celik, Emine; Olson, Eric; Titi, Edriss S. 3 2019 Global well-posedness of a 3D MHD model in porous media. Zbl 1431.76155Titi, Edriss S.; Trabelsi, Saber 2 2019 A data assimilation algorithm: the paradigm of the 3D Leray-\(\alpha\) model of turbulence. Zbl 1436.35274Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 2 2019 A determining form for the subcritical surface quasi-geostrophic equation. Zbl 1420.35042Jolly, Michael S.; Martinez, Vincent R.; Sadigov, Tural; Titi, Edriss S. 2 2019 Onsager’s conjecture for the incompressible Euler equations in bounded domains. Zbl 1390.35241Bardos, Claude; Titi, Edriss S. 22 2018 Uniform-in-time error estimates for the postprocessing Galerkin method applied to a data assimilation algorithm. Zbl 1384.35067Mondaini, Cecilia F.; Titi, Edriss S. 14 2018 Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study. Zbl 1404.76100Farhat, Aseel; Johnston, Hans; Jolly, Michael; Titi, Edriss S. 8 2018 Global stabilization of the Navier-Stokes-voight and the damped nonlinear wave equations by finite number of feedback controllers. Zbl 1402.35043Kalantarov, Varga K.; Titi, Edriss S. 4 2018 Global strong solutions for the three-dimensional Hasegawa-Mima model with partial dissipation. Zbl 1394.76053Cao, Chongsheng; Guo, Yanqiu; Titi, Edriss S. 1 2018 Downscaling the 2D Bénard convection equations using continuous data assimilation. Zbl 1383.65088Altaf, M. U.; Titi, E. S.; Gebrael, T.; Knio, O. M.; Zhao, L.; McCabe, M. F.; Hoteit, I. 22 2017 Finite determining parameters feedback control for distributed nonlinear dissipative systems – a computational study. Zbl 1375.35256Lunasin, Evelyn; Titi, Edriss S. 21 2017 Continuous data assimilation for a 2D Bénard convection system through horizontal velocity measurements alone. Zbl 1365.35108Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 18 2017 A data assimilation algorithm for the subcritical surface quasi-geostrophic equation. Zbl 1358.35091Jolly, Michael S.; Martinez, Vincent R.; Titi, Edriss S. 15 2017 Strong solutions to the 3D primitive equations with only horizontal dissipation: near \(H^{1}\) initial data. Zbl 1366.35123Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 12 2017 Existence and uniqueness of weak solutions to viscous primitive equations for a certain class of discontinuous initial data. Zbl 1364.35275Li, Jinkai; Titi, Edriss S. 11 2017 Global well-posedness for passively transported nonlinear moisture dynamics with phase changes. Zbl 1379.35325Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S. 7 2017 Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equation – Fourier modes case. Zbl 1364.35312Jolly, Michael S.; Sadigov, Tural; Titi, Edriss S. 6 2017 One-dimensional parametric determining form for the two-dimensional Navier-Stokes equations. Zbl 1379.35211Foias, Ciprian; Jolly, Michael S.; Lithio, Dan; Titi, Edriss S. 3 2017 Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Zbl 1336.35297Li, Jinkai; Titi, Edriss S. 34 2016 Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model. Zbl 1339.35246Markowich, Peter A.; Titi, Edriss S.; Trabelsi, Saber 33 2016 A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations. Zbl 1373.76027Gesho, Masakazu; Olson, Eric; Titi, Edriss S. 27 2016 Continuous data assimilation for the three-dimensional Navier-Stokes-\(\alpha\) model. Zbl 1344.35078Albanez, Débora A. F.; Nussenzveig Lopes, Helena J.; Titi, Edriss S. 27 2016 A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. Zbl 1362.35208Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. 24 2016 Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field. Zbl 1334.35202Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 24 2016 Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Zbl 1351.35125Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 21 2016 Global well-posedness of strong solutions to a tropical climate model. Zbl 1339.35325Titi, Edriss; Li, Jinkai 21 2016 Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements. Zbl 1334.35230Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 19 2016 On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in \(\mathbb{R}^2\). Zbl 1332.76013Li, Jinkai; Titi, Edriss S.; Xin, Zhouping 18 2016 On the Charney conjecture of data assimilation employing temperature measurements alone: the paradigm of 3D planetary geostrophic model. Zbl 1364.86017Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. 16 2016 A tropical atmosphere model with moisture: global well-posedness and relaxation limit. Zbl 1345.35116Li, Jinkai; Titi, Edriss S. 9 2016 Finite-parameters feedback control for stabilizing damped nonlinear wave equations. Zbl 1350.35123Kalantarov, Varga K.; Titi, Edriss S. 7 2016 Global regularity versus finite-time singularities: some paradigms on the effect of boundary conditions and certain perturbations. Zbl 1408.35166Larios, Adam; Titi, Edriss S. 4 2016 Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamics. Zbl 1317.35262Cao, Chongsheng; Ibrahim, Slim; Nakanishi, Kenji; Titi, Edriss S. 32 2015 Continuous data assimilation with stochastically noisy data. Zbl 1308.35161Bessaih, Hakima; Olson, Eric; Titi, Edriss S. 32 2015 Continuous data assimilation for the 2D Bénard convection through velocity measurements alone. Zbl 1364.76053Farhat, Aseel; Jolly, Michael S.; Titi, Edriss S. 31 2015 Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers. Zbl 1364.35277Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Titi, Edriss S.; Zang, Aibin 16 2015 A determining form for the damped driven nonlinear Schrödinger equation – Fourier modes case. Zbl 1309.35135Jolly, Michael S.; Sadigov, Tural; Titi, Edriss S. 12 2015 Approximation of 2D Euler equations by the second-grade fluid equations with Dirichlet boundary conditions. Zbl 1328.35153Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Titi, Edriss S.; Zang, Aibin 9 2015 On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S. 8 2015 Inertial manifolds for certain subgrid-scale \(\alpha\)-models of turbulence. Zbl 1328.35150Hamed, Mohammad Abu; Guo, Yanqiu; Titi, Edriss S. 5 2015 Global well-posedness of a system of nonlinearly coupled KdV equations of Majda and Biello. Zbl 1326.35313Guo, Yanqiu; Simon, Konrad; Titi, Edriss S. 4 2015 Continuous data assimilation using general interpolant observables. Zbl 1291.35168Azouani, Abderrahim; Olson, Eric; Titi, Edriss S. 42 2014 Feedback control of nonlinear dissipative systems by finite determining parameters – a reaction-diffusion paradigm. Zbl 1304.35715Azouani, Abderrahim; Titi, Edriss S. 31 2014 Local and global well-posedness of strong solutions to the 3D primitive equations with vertical Eddy diffusivity. Zbl 1305.35113Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 25 2014 Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. Zbl 1300.35089Cao, Chongsheng; Li, Jinkai; Titi, Edriss S. 23 2014 A unified approach to determining forms for the 2D Navier-Stokes equations – the general interpolants case. Zbl 1301.35108Foias, C.; Jolly, M. S.; Kravchenko, R.; Titi, E. S. 14 2014 Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations. Zbl 1307.76083Larios, Adam; Titi, Edriss S. 11 2014 Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping. Zbl 1302.35259Guo, Yanqiu; Rammaha, Mohammad A.; Sakuntasathien, Sawanya; Titi, Edriss S.; Toundykov, Daniel 11 2014 Planar limits of three-dimensional incompressible flows with helical symmetry. Zbl 1312.35144Lopes Filho, Milton C.; Mazzucato, Anna L.; Niu, Dongjuan; Lopes, Helena J. Nussenzveig; Titi, Edriss S. 6 2014 Dissipation length scale estimates for turbulent flows: a Wiener algebra approach. Zbl 1300.35066Biswas, A.; Jolly, M. S.; Martinez, V. R.; Titi, E. S. 4 2014 Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion. Zbl 1284.35343Larios, Adam; Lunasin, Evelyn; Titi, Edriss S. 71 2013 Analysis of a mixture model of tumor growth. Zbl 1292.35153Lowengrub, John; Titi, Edriss; Zhao, Kun 30 2013 Stability of two-dimensional viscous incompressible flows under three-dimensional perturbations and inviscid symmetry breaking. Zbl 1291.35207Bardos, C.; Lopes Filho, M. C.; Niu, Dongjuan; Nussenzveig Lopes, H. J.; Titi, E. S. 24 2013 Persistency of analyticity for nonlinear wave equations: An energy-like approach. Zbl 1298.35022Guo, Yanqiu; Titi, Edriss S. 7 2013 Global well-posedness of an inviscid three-dimensional pseudo-Hasegawa-Mima model. Zbl 1308.35200Cao, Chongsheng; Farhat, Aseel; Titi, Edriss S. 7 2013 The 3D incompressible Euler equations with a passive scalar: a road to blow-up? Zbl 1292.35216Gibbon, John D.; Titi, Edriss S. 5 2013 On the global regularity of a helical-decimated version of the 3D Navier-Stokes equations. Zbl 1275.35057Biferale, Luca; Titi, Edriss S. 5 2013 Global well-posedness of the \(3D\) primitive equations with partial vertical turbulence mixing heat diffusion. Zbl 1267.35157Cao, Chongsheng; Titi, Edriss S. 24 2012 A determining form for the two-dimensional Navier-Stokes equations: the Fourier modes case. Zbl 1426.76103Foias, Ciprian; Jolly, Michael S.; Kravchenko, Rostyslav; Titi, Edriss S. 17 2012 The vanishing viscosity as a selection principle for the Euler equations: the case of 3D shear flow. Zbl 1253.35107Bardos, Claude; Titi, Edriss S.; Wiedemann, Emil 14 2012 Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence. Zbl 1282.86011Farhat, Aseel; Lee Panetta, R.; Titi, Edriss S.; Ziane, Mohammed 1 2012 Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. Zbl 1256.35051Cao, Chongsheng; Titi, Edriss S. 89 2011 On the regularization mechanism for the periodic Korteweg-de Vries equation. Zbl 1284.35365Babin, Anatoli V.; Ilyin, Alexei A.; Titi, Edriss S. 37 2011 Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations. Zbl 1302.76048Hayden, Kevin; Olson, Eric; Titi, Edriss S. 32 2011 Analysis and computation of a discrete KdV-Burgers type equation with fast dispersion and slow diffusion. Zbl 1245.34063Artstein, Zvi; Gear, C. William; Kevrekidis, Ioannis G.; Slemrod, Marshall; Titi, Edriss S. 6 2011 On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models. Zbl 1202.35172Larios, Adam; Titi, Edriss S. 37 2010 Loss of smoothness and energy conserving rough weak solutions for the \(3d\) Euler equations. Zbl 1191.76057Bardos, Claude; Titi, E. S. 23 2010 On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model. Zbl 1188.35135Levant, Boris; Ramos, Fabio; Titi, Edriss S. 22 2010 On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations. Zbl 1375.35348Linshiz, Jasmine S.; Titi, Edriss S. 21 2010 Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit. Zbl 1387.35462Ramos, Fabio; Titi, Edriss S. 17 2010 Entire solutions of hydrodynamical equations with exponential dissipation. Zbl 1208.35100Bardos, Claude; Frisch, Uriel; Pauls, Walter; Ray, Samriddhi Sankar; Titi, Edriss S. 7 2010 Stochastic attractors for shell phenomenological models of turbulence. Zbl 1402.76056Bessaih, Hakima; Flandoli, Franco; Titi, Edriss S. 7 2010 Global regularity and convergence of a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the two-dimensional Euler equations. Zbl 1218.76012Bardos, Claude; Titi, Edriss S.; Linshiz, Jasmine S. 7 2010 Global attractors and determining modes for the 3D Navier-Stokes-Voight equations. Zbl 1178.37112Kalantarov, Varga K.; Titi, Edriss S. 66 2009 Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations. Zbl 1177.35152Kalantarov, Varga K.; Levant, Boris; Titi, Edriss S. 33 2009 Global existence and uniqueness of weak solutions of three-dimensional Euler equations with helical symmetry in the absence of vorticity stretching. Zbl 1303.76006Ettinger, Boris; Titi, Edriss S. 14 2009 On the rate of convergence of the two-dimensional \(\alpha \)-models of turbulence to the Navier-Stokes equations. Zbl 1192.35129Cao, Yanping; Titi, Edriss S. 14 2009 Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation. Zbl 1169.35370Cao, Yanping; Musslimani, Ziad H.; Titi, Edriss S. 4 2009 Simulations of turbulent ocean flow using a deconvolution model. Zbl 1159.76018Bennis, Anne-Claire; Lewandowski, Roger; Titi, Edriss S. 2 2009 Regularity criteria for the three-dimensional Navier-Stokes equations. Zbl 1159.35053Cao, Chongsheng; Titi, Edriss S. 103 2008 A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime. Zbl 1140.35345Kupferman, Raz; Mangoubi, Claude; Titi, Edriss S. 16 2008 Determining modes and Grashof number in 2D turbulence: a numerical case study. Zbl 1178.76190Olson, Eric; Titi, Edriss S. 15 2008 Spectral scaling of the Leray-\(\alpha \) model for two-dimensional turbulence. Zbl 1195.76199Lunasin, Evelyn; Kurien, Susan; Titi, Edriss S. 15 2008 An inviscid regularization for the surface quasi-geostrophic equation. Zbl 1149.35018Khouider, Boualem; Titi, Edriss S. 15 2008 Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence. Zbl 1195.76195Geurts, Bernard J.; Kuczaj, Arkadiusz K.; Titi, Edriss S. 10 2008 Regularity criterion for solutions of three-dimensional turbulent channel flows. Zbl 1151.76012Cao, Chongsheng; Qin, Junlin; Titi, Edriss S. 10 2008 Young measure approach to computing slowly advancing fast oscillations. Zbl 1155.65057Artstein, Zvi; Linshiz, Jasmine; Titi, Edriss S. 9 2008 Nonlinear Schrödinger-Helmholtz equation as numerical regularization of the nonlinear Schrödinger equation. Zbl 1143.35365Cao, Yanping; Musslimani, Ziad H.; Titi, Edriss S. 9 2008 Global regularity for a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the 2D Euler equations. Zbl 1143.76384Bardos, Claude; Linshiz, Jasmine S.; Titi, Edriss S. 7 2008 The damped-driven 2D Navier-Stokes system on large elongated domains. Zbl 1162.76323Ilyin, Alexei A.; Titi, Edriss S. 3 2008 ...and 99 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,277 Authors 115 Titi, Edriss Saleh 34 Rebholz, Leo G. 33 Holm, Darryl D. 32 Tachim Medjo, Theodore 31 Temam, Roger Meyer 30 Jolly, Michael S. 29 Foiaş, Ciprian Ilie 29 Wu, Jiahong 27 Kukavica, Igor 22 Constantin, Peter 22 Gao, Hongjun 22 Ye, Zhuan 21 Guo, Boling 20 Vicol, Vlad C. 17 Duan, Jinqiao 17 Nguyen Huy Tuan 16 Berselli, Luigi Carlo 16 Cao, Chongsheng 16 Zhang, Zujin 15 Bessaih, Hakima 15 Cung The Anh 15 Dong, Boqing 14 He, Yinnian 14 Himonas, A. 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