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Author ID: ilyin.alexei-a Recent zbMATH articles by "Ilyin, Alexei A."
Published as: Ilyin, A. A.; Ilyin, Alexei A.; Ilyin, Alexei; Il’yin, A. A.; Ilyin, A.
Documents Indexed: 51 Publications since 1992
Co-Authors: 17 Co-Authors with 33 Joint Publications
613 Co-Co-Authors
all top 5

Serials

5 Sbornik: Mathematics
3 Mathematical Notes
3 Physica D
3 Discrete and Continuous Dynamical Systems
3 Doklady Mathematics
2 Nonlinearity
2 Russian Mathematical Surveys
2 Journal of the London Mathematical Society. Second Series
1 Communications on Pure and Applied Mathematics
1 Journal of Mathematical Analysis and Applications
1 Bulletin of the London Mathematical Society
1 Functional Analysis and its Applications
1 Journal of Functional Analysis
1 Mathematische Zeitschrift
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Proceedings of the London Mathematical Society. Third Series
1 The Quarterly Journal of Mathematics. Oxford Second Series
1 Differential and Integral Equations
1 IMRN. International Mathematics Research Notices
1 Journal of Dynamics and Differential Equations
1 Journal of Nonlinear Science
1 Russian Journal of Mathematical Physics
1 St. Petersburg Mathematical Journal
1 Journal of Inverse and Ill-Posed Problems
1 Russian Journal of Numerical Analysis and Mathematical Modelling
1 Advances in Differential Equations
1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Journal of Mathematical Fluid Mechanics
1 Discrete and Continuous Dynamical Systems. Series B
1 Communications in Mathematical Sciences
1 Dynamics of Partial Differential Equations
1 Proceedings of the Steklov Institute of Mathematics
1 Journal of Spectral Theory
1 Bulletin of Mathematical Sciences
1 Nonlinear Analysis. Theory, Methods & Applications

Publications by Year

Citations contained in zbMATH Open

41 Publications have been cited 382 times in 247 Documents Cited by Year
A modified-Leray-\(\alpha\) subgrid scale model of turbulence. Zbl 1106.35050
Ilyin, Alexei A.; Lunasin, Evelyn M.; Titi, Edriss S.
59
2006
On the regularization mechanism for the periodic Korteweg-de Vries equation. Zbl 1284.35365
Babin, Anatoli V.; Ilyin, Alexei A.; Titi, Edriss S.
44
2011
Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations. Zbl 1084.35058
Ilyin, A. A.; Miranville, A.; Titi, E. S.
28
2004
On the fractal dimension of invariant sets: Applications to Navier-Stokes equations. Zbl 1049.37047
Chepyzhov, V. V.; Ilyin, A. A.
24
2004
Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations. Zbl 1106.35049
Ilyin, A. A.; Titi, E. S.
23
2006
Attractors for the two-dimensional Navier–Stokes-\({\alpha}\) model: an \({\alpha}\)-dependence study. Zbl 1039.35078
Ilyin, A. A.; Titi, E. S.
21
2003
A note on the fractal dimension of attractors of dissipative dynamical systems. Zbl 1153.37438
Chepyzhov, V. V.; Ilyin, A. A.
19
2001
Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides. Zbl 0877.35093
Ilyin, A. A.
18
1996
On the spectrum of the Stokes operator. Zbl 1185.35165
Ilyin, A. A.
15
2009
Attractors for Navier-Stokes equations in domains with finite measure. Zbl 0859.35090
Ilyin, A. A.
13
1996
Lower bounds for the spectrum of the Laplace and Stokes operators. Zbl 1190.35171
Ilyin, Alexei A.
13
2010
Lieb-Thirring inequalities on the \(N\)-sphere and in the plane, and some applications. Zbl 0789.58079
Ilyin, A. A.
11
1993
Best constants in multiplicative inequalities for sup-norms. Zbl 0923.26011
Ilyin, A. A.
10
1998
Positivity and the attractor dimension in a fourth-order reaction-diffusion equation. Zbl 1056.37085
Bartuccelli, M. V.; Gourley, S. A.; Ilyin, A. A.
9
2002
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
Lieb-Thirring integral inequalities and sharp bounds for the dimension of the attractor of the Navier-Stokes equations with friction. Zbl 1351.35103
Ilyin, A. A.
5
2006
Asymptotically sharp multiplicative inequalities. Zbl 0840.46018
Edmunds, D. E.; Ilyin, A. A.
5
1995
Lieb-Thirring inequalities on some manifolds. Zbl 1308.58004
Ilyin, Alexei A.
5
2012
The damped-driven 2D Navier-Stokes system on large elongated domains. Zbl 1162.76323
Ilyin, Alexei A.; Titi, Edriss S.
4
2008
On some multiplicative inequalities and approximation numbers. Zbl 0818.46027
Edmunds, D. E.; Ilyin, A. A.
4
1994
Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051
Zelik, S. V.; Ilyin, A. A.
4
2014
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
4
2016
Navier-Stokes equations on the rotating sphere. A simple proof of the attractor dimension estimate. Zbl 0840.35077
Ilyin, A. A.
4
1994
Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036
Ilyin, Alexei; Patni, Kavita; Zelik, Sergey
4
2016
On the domain of analyticity and small scales for the solutions of the damped-driven 2D Navier-Stokes equations. Zbl 1132.35318
Ilyin, Alexei A.; Titi, Edriss S.
3
2007
Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145
Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey
3
2018
Strong trajectory and global \(\mathbf{W^{1,p}}\)-attractors for the damped-driven Euler system in \(\mathbb R^2\). Zbl 1359.35013
Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir
3
2017
Best constants in Sobolev inequalities on the sphere and in Euclidean space. Zbl 0922.46032
Ilyin, A. A.
2
1999
On the dimension of attractors for Navier-Stokes equations on two- dimensional compact manifolds. Zbl 0771.35045
Ilyin, Alexei A.
2
1993
Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147
Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey
2
2018
On the closeness of trajectories for model quasi-gasdynamic equations. Zbl 1360.35180
Ilyin, A. A.; Rykov, Yu. G.
2
2016
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101
Ilyin, Alexei A.; Zelik, Sergey
2
2021
Some dimensionless numbers and the associated inequalities describing the asymptotic behaviour of the solutions to the barotropic vorticity equation. Zbl 0820.76036
Ilyin, A. A.
1
1992
Best constants in the class of polymultiplicative inequalities for derivatives. Zbl 0923.46036
Il’yin, A. A.
1
1998
On strong convergence of attractors of Navier-Stokes equations in the limit of vanishing viscosity. Zbl 1371.35197
Ilyin, A. A.; Chepyzhov, V. V.
1
2017
Analysis of ill-posedness and numerical methods of solving a nonlinear inverse problem in pharmacokinetics for the two-compartmental model with extravascular drug administration. Zbl 1279.92008
Ilyin, A.; Kabanikhin, S. I.; Nurseitov, D. B.; Nurseitova, A. T.; Asmanova, N. A.; Voronov, D. A.; Bakytov, D.
1
2012
Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196
Ilyin, Alexei; Laptev, Ari; Zelik, Sergey
1
2020
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
Magnetic Lieb-Thirring inequality for periodic functions. Zbl 1453.35007
Ilyin, A. A.; Laptev, A. A.
1
2020
Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149
Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G.
1
2021
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101
Ilyin, Alexei A.; Zelik, Sergey
2
2021
Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149
Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G.
1
2021
Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196
Ilyin, Alexei; Laptev, Ari; Zelik, Sergey
1
2020
Lieb-Thirring inequalities on the sphere. Zbl 1450.35195
Ilyin, A.; Laptev, A.
1
2020
Magnetic Lieb-Thirring inequality for periodic functions. Zbl 1453.35007
Ilyin, A. A.; Laptev, A. A.
1
2020
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
1
2019
Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145
Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey
3
2018
Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147
Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey
2
2018
Strong trajectory and global \(\mathbf{W^{1,p}}\)-attractors for the damped-driven Euler system in \(\mathbb R^2\). Zbl 1359.35013
Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir
3
2017
On strong convergence of attractors of Navier-Stokes equations in the limit of vanishing viscosity. Zbl 1371.35197
Ilyin, A. A.; Chepyzhov, V. V.
1
2017
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
8
2016
Lieb-Thirring inequalities on the torus. Zbl 1365.35096
Ilyin, Alexei A.; Laptev, Ari A.
4
2016
Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036
Ilyin, Alexei; Patni, Kavita; Zelik, Sergey
4
2016
On the closeness of trajectories for model quasi-gasdynamic equations. Zbl 1360.35180
Ilyin, A. A.; Rykov, Yu. G.
2
2016
Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051
Zelik, S. V.; Ilyin, A. A.
4
2014
Lieb-Thirring inequalities on some manifolds. Zbl 1308.58004
Ilyin, Alexei A.
5
2012
Analysis of ill-posedness and numerical methods of solving a nonlinear inverse problem in pharmacokinetics for the two-compartmental model with extravascular drug administration. Zbl 1279.92008
Ilyin, A.; Kabanikhin, S. I.; Nurseitov, D. B.; Nurseitova, A. T.; Asmanova, N. A.; Voronov, D. A.; Bakytov, D.
1
2012
On the regularization mechanism for the periodic Korteweg-de Vries equation. Zbl 1284.35365
Babin, Anatoli V.; Ilyin, Alexei A.; Titi, Edriss S.
44
2011
Lower bounds for the spectrum of the Laplace and Stokes operators. Zbl 1190.35171
Ilyin, Alexei A.
13
2010
On the spectrum of the Stokes operator. Zbl 1185.35165
Ilyin, A. A.
15
2009
The damped-driven 2D Navier-Stokes system on large elongated domains. Zbl 1162.76323
Ilyin, Alexei A.; Titi, Edriss S.
4
2008
On the domain of analyticity and small scales for the solutions of the damped-driven 2D Navier-Stokes equations. Zbl 1132.35318
Ilyin, Alexei A.; Titi, Edriss S.
3
2007
A modified-Leray-\(\alpha\) subgrid scale model of turbulence. Zbl 1106.35050
Ilyin, Alexei A.; Lunasin, Evelyn M.; Titi, Edriss S.
59
2006
Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations. Zbl 1106.35049
Ilyin, A. A.; Titi, E. S.
23
2006
Lieb-Thirring integral inequalities and sharp bounds for the dimension of the attractor of the Navier-Stokes equations with friction. Zbl 1351.35103
Ilyin, A. A.
5
2006
Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations. Zbl 1084.35058
Ilyin, A. A.; Miranville, A.; Titi, E. S.
28
2004
On the fractal dimension of invariant sets: Applications to Navier-Stokes equations. Zbl 1049.37047
Chepyzhov, V. V.; Ilyin, A. A.
24
2004
Attractors for the two-dimensional Navier–Stokes-\({\alpha}\) model: an \({\alpha}\)-dependence study. Zbl 1039.35078
Ilyin, A. A.; Titi, E. S.
21
2003
Positivity and the attractor dimension in a fourth-order reaction-diffusion equation. Zbl 1056.37085
Bartuccelli, M. V.; Gourley, S. A.; Ilyin, A. A.
9
2002
A note on the fractal dimension of attractors of dissipative dynamical systems. Zbl 1153.37438
Chepyzhov, V. V.; Ilyin, A. A.
19
2001
Best constants in Sobolev inequalities on the sphere and in Euclidean space. Zbl 0922.46032
Ilyin, A. A.
2
1999
Best constants in multiplicative inequalities for sup-norms. Zbl 0923.26011
Ilyin, A. A.
10
1998
Best constants in the class of polymultiplicative inequalities for derivatives. Zbl 0923.46036
Il’yin, A. A.
1
1998
Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides. Zbl 0877.35093
Ilyin, A. A.
18
1996
Attractors for Navier-Stokes equations in domains with finite measure. Zbl 0859.35090
Ilyin, A. A.
13
1996
Asymptotically sharp multiplicative inequalities. Zbl 0840.46018
Edmunds, D. E.; Ilyin, A. A.
5
1995
On some multiplicative inequalities and approximation numbers. Zbl 0818.46027
Edmunds, D. E.; Ilyin, A. A.
4
1994
Navier-Stokes equations on the rotating sphere. A simple proof of the attractor dimension estimate. Zbl 0840.35077
Ilyin, A. A.
4
1994
Lieb-Thirring inequalities on the \(N\)-sphere and in the plane, and some applications. Zbl 0789.58079
Ilyin, A. A.
11
1993
On the dimension of attractors for Navier-Stokes equations on two- dimensional compact manifolds. Zbl 0771.35045
Ilyin, Alexei A.
2
1993
Some dimensionless numbers and the associated inequalities describing the asymptotic behaviour of the solutions to the barotropic vorticity equation. Zbl 0820.76036
Ilyin, A. A.
1
1992
all top 5

Cited by 300 Authors

20 Ilyin, Alexei A.
19 Titi, Edriss Saleh
17 Zelik, Sergey V.
10 Chepyzhov, Vladimir V.
9 Oh, Tadahiro
8 Laptev, Ari
7 Bartuccelli, Michele V.
5 Vishik, Marko Iosifovich
4 Berselli, Luigi Carlo
4 Chen, Caisheng
4 Cung The Anh
4 Kostianko, Anna
4 Langa, Jose’ Antonio
4 Lewandowski, Roger
4 Pattakos, Nikolaos
4 Radkevich, Evgeniĭ Vladimirovich
4 Rebholz, Leo G.
4 Tzvetkov, Nikolay
4 Wu, Delin
4 Yolcu, Selma Yıldırım
4 Yolcu, Turkay
3 Erdoğan, Mehmet Burak
3 Gubinelli, Massimiliano
3 Ibrahim, Slim
3 Kunstmann, Peer Christian
3 Kwon, Soonsik
3 Larios, Adam
3 Linshiz, Jasmine S.
3 Lunasin, Evelyn M.
3 Manica, Carolina Cardoso
3 Mohan, Manil Thankamani
3 Pei, Yuan
3 Phan, Duy Nhat
3 Qiu, Hua
3 Real Anguas, José
3 Robinson, James Cooper
3 Smyth, Noel Frederick
3 Tzirakis, Nikolaos
3 Yoon, Haewon
3 Zvyagin, Andreĭ Viktorovich
2 Ali, Hani
2 Bardos, Claude Williams
2 Bisconti, Luca
2 Caraballo Garrido, Tomás
2 Catania, Davide
2 Chai, Xiaojuan
2 Chaichenets, Leonid
2 Climent-Ezquerra, Blanca
2 Constantin, Peter
2 Correia, Simão
2 Deugoue, Gabriel
2 Du, Yi
2 Duan, Yonghong
2 Dunca, Argus Adrian
2 Gal, Ciprian Gheorghe Sorin
2 Goubet, Olivier
2 Guo, Yanqiu
2 Guo, Zihua
2 Gürel, T. Burak
2 Hundertmark, Dirk
2 Jin, Chunhua
2 Kalantarov, Varga K.
2 Kyrychko, Yuliya N.
2 Layton, William J.
2 Levant, Boris
2 Li, Xinhua
2 Lin, Quyuan
2 Lu, Yongjin
2 Łukaszewicz, Grzegorz
2 Ma, Caochuan
2 Ma, To Fu
2 Marquez-Duran, Antonio M.
2 Molinet, Luc
2 Olson, Eric J.
2 Polyakov, Dmitriĭ Mikhaĭlovich
2 Razafimandimby, Paul André
2 Rodrigues, Sérgio S.
2 Rojas-Medar, Marko Antonio
2 Shen, Chun
2 Song, Hongxue
2 Sun, Chunyou
2 Toi, Vu Manh
2 Tran, Chuong V.
2 Tsutsumi, Yoshio
2 Wang, Yuzhao
2 Wirosoetisno, Djoko
2 Yang, Xinguang
2 Yao, Zhengan
2 Yi, Lijun
2 Yue, Gaocheng
2 Zhao, Xiaopeng
2 Zhong, Chengkui
1 Anguiano, María
1 Argatov, Ivan I.
1 Argyropoulos, C. D.
1 Assanto, Gaetano
1 Bach, Bui Huy
1 Băleanu, Dumitru I.
1 Barreira, Luis Manuel
1 Bessaih, Hakima
...and 200 more Authors
all top 5

Cited in 118 Serials

16 Physica D
12 Journal of Mathematical Analysis and Applications
11 Journal of Mathematical Fluid Mechanics
9 Journal of Mathematical Physics
9 Journal of Differential Equations
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 Discrete and Continuous Dynamical Systems. Series B
5 Communications in Mathematical Physics
5 Journal of Functional Analysis
5 Doklady Mathematics
4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
4 Applied Mathematics Letters
4 Journal of Mathematical Sciences (New York)
4 Discrete and Continuous Dynamical Systems
4 Nonlinear Analysis. Real World Applications
4 Evolution Equations and Control Theory
3 Mathematical Methods in the Applied Sciences
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Journal of Computational and Applied Mathematics
3 Journal of Dynamics and Differential Equations
3 Journal of Nonlinear Science
3 Topological Methods in Nonlinear Analysis
3 Abstract and Applied Analysis
2 Applicable Analysis
2 Mathematical Notes
2 Nonlinearity
2 Annales Polonici Mathematici
2 Applied Mathematics and Optimization
2 Acta Applicandae Mathematicae
2 Revista Matemática Iberoamericana
2 Applied Mathematical Modelling
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 SIAM Journal on Mathematical Analysis
2 Stochastic Processes and their Applications
2 Russian Journal of Mathematical Physics
2 Physics of Fluids
2 Sbornik: Mathematics
2 Mathematical Physics, Analysis and Geometry
2 Discrete Dynamics in Nature and Society
2 Communications in Contemporary Mathematics
2 Communications on Pure and Applied Analysis
2 SIAM Journal on Applied Dynamical Systems
2 Mediterranean Journal of Mathematics
2 Science China. Mathematics
2 Forum of Mathematics, Sigma
1 Acta Mechanica
1 Archive for Rational Mechanics and Analysis
1 Computers and Fluids
1 Computers & Mathematics with Applications
1 Computer Methods in Applied Mechanics and Engineering
1 Journal d’Analyse Mathématique
1 Journal of Statistical Physics
1 Physics Letters. A
1 Russian Mathematical Surveys
1 Mathematics of Computation
1 Theoretical and Computational Fluid Dynamics
1 Applied Mathematics and Computation
1 Czechoslovak Mathematical Journal
1 Duke Mathematical Journal
1 Functional Analysis and its Applications
1 Indiana University Mathematics Journal
1 Inventiones Mathematicae
1 Mathematische Annalen
1 Mathematische Nachrichten
1 Monatshefte für Mathematik
1 Numerical Functional Analysis and Optimization
1 Proceedings of the American Mathematical Society
1 SIAM Journal on Numerical Analysis
1 Transactions of the American Mathematical Society
1 Ergodic Theory and Dynamical Systems
1 Chinese Annals of Mathematics. Series B
1 Acta Mathematicae Applicatae Sinica. English Series
1 Optimization
1 Probability Theory and Related Fields
1 Numerical Methods for Partial Differential Equations
1 Journal of Theoretical Probability
1 Journal of Scientific Computing
1 Applications of Mathematics
1 Computational Mathematics and Mathematical Physics
1 Communications in Partial Differential Equations
1 Expositiones Mathematicae
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Russian Mathematics
1 Potential Analysis
1 St. Petersburg Mathematical Journal
1 Computational and Applied Mathematics
1 Fractals
1 Advances in Computational Mathematics
1 Electronic Research Announcements of the American Mathematical Society
1 The Journal of Fourier Analysis and Applications
1 Mathematical Problems in Engineering
1 International Journal of Computational Fluid Dynamics
1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
1 Revista Matemática Complutense
1 Annals of Mathematics. Second Series
1 Communications in Nonlinear Science and Numerical Simulation
1 Journal of Dynamical and Control Systems
1 Journal of Turbulence
1 Journal of Evolution Equations
...and 18 more Serials

Citations by Year