Nguyen, Vinh; Shvydkoy, Roman Continuous model of opinion dynamics with convictions. (English) Zbl 1528.91059 Discrete Contin. Dyn. Syst. 43, No. 11, 4010-4026 (2023). Reviewer: Yilun Shang (Newcastle upon Tyne) MSC: 91D30 35Q49 PDFBibTeX XMLCite \textit{V. Nguyen} and \textit{R. Shvydkoy}, Discrete Contin. Dyn. Syst. 43, No. 11, 4010--4026 (2023; Zbl 1528.91059) Full Text: DOI arXiv
Cheskidov, Alexey; Shvydkoy, Roman Volumetric theory of intermittency in fully developed turbulence. (English) Zbl 1512.76040 Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 45, 35 p. (2023). MSC: 76F02 76F55 35Q35 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, Arch. Ration. Mech. Anal. 247, No. 3, Paper No. 45, 35 p. (2023; Zbl 1512.76040) Full Text: DOI arXiv
Nguyen, Vinh; Shvydkoy, Roman Propagation of chaos for the Cucker-Smale systems under heavy tail communication. (English) Zbl 1501.35415 Commun. Partial Differ. Equations 47, No. 9, 1883-1906 (2022). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35Q92 35Q35 92D25 35F20 34A12 PDFBibTeX XMLCite \textit{V. Nguyen} and \textit{R. Shvydkoy}, Commun. Partial Differ. Equations 47, No. 9, 1883--1906 (2022; Zbl 1501.35415) Full Text: DOI arXiv
Shvydkoy, Roman Global hypocoercivity of kinetic Fokker-Planck-alignment equations. (English) Zbl 1486.35386 Kinet. Relat. Models 15, No. 2, 213-237 (2022). MSC: 35Q84 35Q35 92D25 PDFBibTeX XMLCite \textit{R. Shvydkoy}, Kinet. Relat. Models 15, No. 2, 213--237 (2022; Zbl 1486.35386) Full Text: DOI arXiv
Lear, Daniel; Leslie, Trevor M.; Shvydkoy, Roman; Tadmor, Eitan Geometric structure of mass concentration sets for pressureless Euler alignment systems. (English) Zbl 1490.35330 Adv. Math. 401, Article ID 108290, 30 p. (2022). MSC: 35Q35 76N10 35B35 35A01 35A02 PDFBibTeX XMLCite \textit{D. Lear} et al., Adv. Math. 401, Article ID 108290, 30 p. (2022; Zbl 1490.35330) Full Text: DOI arXiv
Lear, Daniel; Reynolds, David N.; Shvydkoy, Roman Global solutions to multi-dimensional topological Euler alignment systems. (English) Zbl 1485.92181 Ann. PDE 8, No. 1, Paper No. 1, 43 p. (2022). MSC: 92D50 35Q35 PDFBibTeX XMLCite \textit{D. Lear} et al., Ann. PDE 8, No. 1, Paper No. 1, 43 p. (2022; Zbl 1485.92181) Full Text: DOI arXiv
Shvydkoy, Roman Environmental Averaging. arXiv:2211.00117 Preprint, arXiv:2211.00117 [math.AP] (2022). MSC: 35Q84 35Q35 92D25 92D50 BibTeX Cite \textit{R. Shvydkoy}, ``Environmental Averaging'', Preprint, arXiv:2211.00117 [math.AP] (2022) Full Text: arXiv OA License
Lear, Daniel; Shvydkoy, Roman Unidirectional flocks in hydrodynamic Euler alignment system. II: Singular models. (English) Zbl 1476.35204 Commun. Math. Sci. 19, No. 3, 807-828 (2021). MSC: 35Q35 76N10 92D25 PDFBibTeX XMLCite \textit{D. Lear} and \textit{R. Shvydkoy}, Commun. Math. Sci. 19, No. 3, 807--828 (2021; Zbl 1476.35204) Full Text: DOI arXiv
Dietert, Helge; Shvydkoy, Roman On Cucker-Smale dynamical systems with degenerate communication. (English) Zbl 1471.92398 Anal. Appl., Singap. 19, No. 4, 551-573 (2021). MSC: 92D50 35Q35 PDFBibTeX XMLCite \textit{H. Dietert} and \textit{R. Shvydkoy}, Anal. Appl., Singap. 19, No. 4, 551--573 (2021; Zbl 1471.92398) Full Text: DOI arXiv
Shvydkoy, Roman; Tadmor, Eitan Multiflocks: emergent dynamics in systems with multiscale collective behavior. (English) Zbl 1470.92403 Multiscale Model. Simul. 19, No. 2, 1115-1141 (2021). MSC: 92D50 35Q35 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{E. Tadmor}, Multiscale Model. Simul. 19, No. 2, 1115--1141 (2021; Zbl 1470.92403) Full Text: DOI arXiv
Shvydkoy, Roman Dynamics and analysis of alignment models of collective behavior. (English) Zbl 1471.37001 Nečas Center Series. Cham: Birkhäuser (ISBN 978-3-030-68146-3/pbk; 978-3-030-68147-0/ebook). xiv, 208 p. (2021). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 37-02 35-02 76-02 37Lxx 76Mxx 35Qxx PDFBibTeX XMLCite \textit{R. Shvydkoy}, Dynamics and analysis of alignment models of collective behavior. Cham: Birkhäuser (2021; Zbl 1471.37001) Full Text: DOI
Shvydkoy, Roman; Tadmor, Eitan Topologically based fractional diffusion and emergent dynamics with short-range interactions. (English) Zbl 1453.92371 SIAM J. Math. Anal. 52, No. 6, 5792-5839 (2020). MSC: 92D50 35Q92 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{E. Tadmor}, SIAM J. Math. Anal. 52, No. 6, 5792--5839 (2020; Zbl 1453.92371) Full Text: DOI arXiv
Constantin, Peter; Drivas, Theodore D.; Shvydkoy, Roman Entropy hierarchies for equations of compressible fluids and self-organized dynamics. (English) Zbl 1444.92139 SIAM J. Math. Anal. 52, No. 3, 3073-3092 (2020). MSC: 92D50 35Q35 76N10 PDFBibTeX XMLCite \textit{P. Constantin} et al., SIAM J. Math. Anal. 52, No. 3, 3073--3092 (2020; Zbl 1444.92139) Full Text: DOI arXiv
Leslie, Trevor M.; Shvydkoy, Roman On the structure of limiting flocks in hydrodynamic Euler alignment models. (English) Zbl 1428.92130 Math. Models Methods Appl. Sci. 29, No. 13, 2419-2431 (2019). MSC: 92D50 35Q92 PDFBibTeX XMLCite \textit{T. M. Leslie} and \textit{R. Shvydkoy}, Math. Models Methods Appl. Sci. 29, No. 13, 2419--2431 (2019; Zbl 1428.92130) Full Text: DOI arXiv
Shvydkoy, Roman Global existence and stability of nearly aligned flocks. (English) Zbl 1426.92094 J. Dyn. Differ. Equations 31, No. 4, 2165-2175 (2019). MSC: 92D50 35Q35 76N10 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Dyn. Differ. Equations 31, No. 4, 2165--2175 (2019; Zbl 1426.92094) Full Text: DOI arXiv
Imbert, Cyril; Jin, Tianling; Shvydkoy, Roman Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation. (English. French summary) Zbl 1471.45008 Ann. Fac. Sci. Toulouse, Math. (6) 27, No. 4, 667-677 (2018). MSC: 45K05 35R09 PDFBibTeX XMLCite \textit{C. Imbert} et al., Ann. Fac. Sci. Toulouse, Math. (6) 27, No. 4, 667--677 (2018; Zbl 1471.45008) Full Text: DOI arXiv
Shvydkoy, Roman; Tadmor, Eitan Eulerian dynamics with a commutator forcing. III: Fractional diffusion of order \(0 < \alpha < 1\). (English) Zbl 1398.35157 Physica D 376-377, 131-137 (2018). MSC: 35Q31 76R50 35A01 35A02 35R11 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{E. Tadmor}, Physica D 376--377, 131--137 (2018; Zbl 1398.35157) Full Text: DOI arXiv
Shvydkoy, Roman On the Rayleigh-Taylor instability in presence of a background shear. (English) Zbl 1397.76045 J. Math. Fluid Mech. 20, No. 3, 1195-1211 (2018). MSC: 76E20 35P05 47D06 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Math. Fluid Mech. 20, No. 3, 1195--1211 (2018; Zbl 1397.76045) Full Text: DOI arXiv
Leslie, Trevor M.; Shvydkoy, Roman The energy measure for the Euler and Navier-Stokes equations. (English) Zbl 1405.35141 Arch. Ration. Mech. Anal. 230, No. 2, 459-492 (2018). MSC: 35Q30 35B44 76D05 35R06 PDFBibTeX XMLCite \textit{T. M. Leslie} and \textit{R. Shvydkoy}, Arch. Ration. Mech. Anal. 230, No. 2, 459--492 (2018; Zbl 1405.35141) Full Text: DOI arXiv
Leslie, Trevor M.; Shvydkoy, Roman Conditions implying energy equality for weak solutions of the Navier-Stokes equations. (English) Zbl 1387.76102 SIAM J. Math. Anal. 50, No. 1, 870-890 (2018). MSC: 76S05 35Q35 PDFBibTeX XMLCite \textit{T. M. Leslie} and \textit{R. Shvydkoy}, SIAM J. Math. Anal. 50, No. 1, 870--890 (2018; Zbl 1387.76102) Full Text: DOI arXiv
Shvydkoy, Roman Homogeneous solutions to the 3D Euler system. (English) Zbl 1386.35333 Trans. Am. Math. Soc. 370, No. 4, 2517-2535 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q31 76B99 37J45 PDFBibTeX XMLCite \textit{R. Shvydkoy}, Trans. Am. Math. Soc. 370, No. 4, 2517--2535 (2018; Zbl 1386.35333) Full Text: DOI arXiv
Shvydkoy, Roman; Tadmor, Eitan Eulerian dynamics with a commutator forcing. (English) Zbl 1379.35252 Trans. Math. Appl. 1, Article ID tnx001, 26 p. (2017). MSC: 35Q35 76N10 92D25 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{E. Tadmor}, Trans. Math. Appl. 1, Article ID tnx001, 26 p. (2017; Zbl 1379.35252) Full Text: DOI arXiv
Shvydkoy, Roman; Tadmor, Eitan Eulerian dynamics with a commutator forcing. II: Flocking. (English) Zbl 1372.35227 Discrete Contin. Dyn. Syst. 37, No. 11, 5503-5520 (2017). MSC: 35Q31 76N10 92D25 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{E. Tadmor}, Discrete Contin. Dyn. Syst. 37, No. 11, 5503--5520 (2017; Zbl 1372.35227) Full Text: DOI arXiv
Constantin, Peter; Gancedo, Francisco; Shvydkoy, Roman; Vicol, Vlad Global regularity for 2D Muskat equations with finite slope. (English) Zbl 1365.76304 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 4, 1041-1074 (2017). MSC: 76S05 35Q35 PDFBibTeX XMLCite \textit{P. Constantin} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 4, 1041--1074 (2017; Zbl 1365.76304) Full Text: DOI arXiv
Luo, Xue; Shvydkoy, Roman Addendum: 2D homogeneous solutions to the Euler equation. (English) Zbl 1430.35191 Commun. Partial Differ. Equations 42, No. 3, 491-493 (2017). MSC: 35Q31 35B65 35C06 76B03 PDFBibTeX XMLCite \textit{X. Luo} and \textit{R. Shvydkoy}, Commun. Partial Differ. Equations 42, No. 3, 491--493 (2017; Zbl 1430.35191) Full Text: DOI arXiv
Imbert, Cyril; Shvydkoy, Roman; Vigneron, François Global well-posedness of a non-local Burgers equation: the periodic case. (English. French summary) Zbl 1355.35190 Ann. Fac. Sci. Toulouse, Math. (6) 25, No. 4, 723-758 (2016). MSC: 35R09 35B30 PDFBibTeX XMLCite \textit{C. Imbert} et al., Ann. Fac. Sci. Toulouse, Math. (6) 25, No. 4, 723--758 (2016; Zbl 1355.35190) Full Text: DOI arXiv
Cheskidov, A.; Lopes Filho, M. C.; Nussenzveig Lopes, H. J.; Shvydkoy, R. Energy conservation in two-dimensional incompressible ideal fluids. (English) Zbl 1351.35112 Commun. Math. Phys. 348, No. 1, 129-143 (2016). MSC: 35Q31 35Q30 76F02 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., Commun. Math. Phys. 348, No. 1, 129--143 (2016; Zbl 1351.35112) Full Text: DOI
Leslie, T. M.; Shvydkoy, R. The energy balance relation for weak solutions of the density-dependent Navier-Stokes equations. (English) Zbl 1383.76080 J. Differ. Equations 261, No. 6, 3719-3733 (2016). MSC: 76D05 35D30 35Q35 76D03 76F99 PDFBibTeX XMLCite \textit{T. M. Leslie} and \textit{R. Shvydkoy}, J. Differ. Equations 261, No. 6, 3719--3733 (2016; Zbl 1383.76080) Full Text: DOI arXiv
Bronzi, Anne; Shvydkoy, Roman On the energy behavior of locally self-similar blowup for the Euler equation. (English) Zbl 1328.76009 Indiana Univ. Math. J. 64, No. 5, 1291-1302 (2015). MSC: 76B03 35Q31 PDFBibTeX XMLCite \textit{A. Bronzi} and \textit{R. Shvydkoy}, Indiana Univ. Math. J. 64, No. 5, 1291--1302 (2015; Zbl 1328.76009) Full Text: DOI arXiv
Luo, Xue; Shvydkoy, Roman 2D homogeneous solutions to the Euler equation. (English) Zbl 1329.35237 Commun. Partial Differ. Equations 40, No. 9, 1666-1687 (2015). MSC: 35Q31 76B03 37J45 35B65 35C06 PDFBibTeX XMLCite \textit{X. Luo} and \textit{R. Shvydkoy}, Commun. Partial Differ. Equations 40, No. 9, 1666--1687 (2015; Zbl 1329.35237) Full Text: DOI arXiv
Cheskidov, A.; Shvydkoy, R. A unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov’s dissipation range. (English) Zbl 1433.76031 J. Math. Fluid Mech. 16, No. 2, 263-273 (2014). MSC: 76D03 76B03 35Q30 35Q31 76F02 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, J. Math. Fluid Mech. 16, No. 2, 263--273 (2014; Zbl 1433.76031) Full Text: DOI arXiv
Cheskidov, A.; Shvydkoy, R. Euler equations and turbulence: analytical approach to intermittency. (English) Zbl 1295.76010 SIAM J. Math. Anal. 46, No. 1, 353-374 (2014). Reviewer: M. Marin (Brasov) MSC: 76F02 35Q31 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, SIAM J. Math. Anal. 46, No. 1, 353--374 (2014; Zbl 1295.76010) Full Text: DOI arXiv
Chae, Dongho; Shvydkoy, Roman On formation of a locally self-similar collapse in the incompressible Euler equations. (English) Zbl 1285.35070 Arch. Ration. Mech. Anal. 209, No. 3, 999-1017 (2013). Reviewer: Gheorghe Moroşanu (Budapest) MSC: 35Q31 35B44 PDFBibTeX XMLCite \textit{D. Chae} and \textit{R. Shvydkoy}, Arch. Ration. Mech. Anal. 209, No. 3, 999--1017 (2013; Zbl 1285.35070) Full Text: DOI arXiv
Shvydkoy, Roman A study of energy concentration and drain in incompressible fluids. (English) Zbl 1322.76012 Nonlinearity 26, No. 2, 425-436 (2013). MSC: 76B03 35Q31 35B44 35B65 35C06 PDFBibTeX XMLCite \textit{R. Shvydkoy}, Nonlinearity 26, No. 2, 425--436 (2013; Zbl 1322.76012) Full Text: DOI arXiv
Cheskidov, Alexey; Shvydkoy, Roman; Friedlander, Susan A continuous model for turbulent energy cascade. (English) Zbl 1296.76059 Robinson, James C. (ed.) et al., Mathematical aspects of fluid mechanics. Selected papers based on the presentations at the workshop partial differential equations and fluid mechanics, Warwick, UK, June 15–19, 2010. Cambridge: Cambridge University Press (ISBN 978-1-107-60925-9/pbk). London Mathematical Society Lecture Note Series 402, 52-69 (2012). MSC: 76F02 35Q35 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., Lond. Math. Soc. Lect. Note Ser. 402, 52--69 (2012; Zbl 1296.76059) Full Text: arXiv
Cheskidov, A.; Shvydkoy, R. Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces. (English) Zbl 1426.76089 J. Math. Phys. 53, No. 11, 115620, 7 p. (2012). MSC: 76D03 35Q30 26A33 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, J. Math. Phys. 53, No. 11, 115620, 7 p. (2012; Zbl 1426.76089) Full Text: DOI arXiv
Shvydkoy, R. Convex integration for a class of active scalar equations. (English) Zbl 1231.35177 J. Am. Math. Soc. 24, No. 4, 1159-1174 (2011). Reviewer: V. D. Sharma (Mumbai) MSC: 35Q35 76W05 35A01 35B10 35D30 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Am. Math. Soc. 24, No. 4, 1159--1174 (2011; Zbl 1231.35177) Full Text: DOI arXiv
Cheskidov, Alexey; Friedlander, Susan; Shvydkoy, Roman On the energy equality for weak solutions of the 3D Navier-Stokes equations. (English) Zbl 1374.35279 Rannacher, Rolf (ed.) et al., Advances in mathematical fluid mechanics. Dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday. Selected papers of the international conference on mathematical fluid mechanics, Estoril, Portugal, May 21–25, 2007. Berlin: Springer (ISBN 978-3-642-04067-2/hbk; 978-3-642-04068-9/ebook). 171-175 (2010). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., in: Advances in mathematical fluid mechanics. Dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday. Selected papers of the international conference on mathematical fluid mechanics, Estoril, Portugal, May 21--25, 2007. Berlin: Springer. 171--175 (2010; Zbl 1374.35279) Full Text: DOI arXiv
Bulíček, Miroslav; Feireisl, Eduard; Málek, Josef; Shvydkoy, Roman On the motion of incompressible inhomogeneous Euler-Korteweg fluids. (English) Zbl 1210.76012 Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 497-515 (2010). MSC: 76A05 35A01 PDFBibTeX XMLCite \textit{M. Bulíček} et al., Discrete Contin. Dyn. Syst., Ser. S 3, No. 3, 497--515 (2010; Zbl 1210.76012) Full Text: DOI
Shvydkoy, Roman Continuous spectrum of the 3D Euler equation is a solid annulus. (Le spectre continu de l’equation d’Euler 3D est un anneau.) (English) Zbl 1198.35160 C. R., Math., Acad. Sci. Paris 348, No. 15-16, 897-900 (2010). MSC: 35P05 35Q31 35A24 PDFBibTeX XMLCite \textit{R. Shvydkoy}, C. R., Math., Acad. Sci. Paris 348, No. 15--16, 897--900 (2010; Zbl 1198.35160) Full Text: DOI arXiv
Cheskidov, A.; Shvydkoy, R. Ill-posedness of the basic equations of fluid dynamics in Besov spaces. (English) Zbl 1423.76085 Proc. Am. Math. Soc. 138, No. 3, 1059-1067 (2010). MSC: 76D03 35Q31 35Q30 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, Proc. Am. Math. Soc. 138, No. 3, 1059--1067 (2010; Zbl 1423.76085) Full Text: DOI arXiv
Cheskidov, A.; Shvydkoy, R. The regularity of weak solutions of the 3D Navier-Stokes equations in \(B^{-1}_{\infty,\infty}\). (English) Zbl 1186.35137 Arch. Ration. Mech. Anal. 195, No. 1, 159-169 (2010). MSC: 35Q30 76D03 76D05 35B65 35D30 PDFBibTeX XMLCite \textit{A. Cheskidov} and \textit{R. Shvydkoy}, Arch. Ration. Mech. Anal. 195, No. 1, 159--169 (2010; Zbl 1186.35137) Full Text: DOI arXiv
Shvydkoy, R.; Latushkin, Y. Operator algebras and the Fredholm spectrum of advective equations of linear hydrodynamics. (English) Zbl 1181.35181 J. Funct. Anal. 257, No. 10, 3309-3328 (2009). MSC: 35Q31 76D33 47G30 47H20 35S05 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{Y. Latushkin}, J. Funct. Anal. 257, No. 10, 3309--3328 (2009; Zbl 1181.35181) Full Text: DOI
Shvydkoy, R. A geometric condition implying an energy equality for solutions of the 3D Navier-Stokes equation. (English) Zbl 1160.76011 J. Dyn. Differ. Equations 21, No. 1, 117-125 (2009). MSC: 76D03 35Q30 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Dyn. Differ. Equations 21, No. 1, 117--125 (2009; Zbl 1160.76011) Full Text: DOI arXiv
Shvydkoy, Roman On the energy of inviscid singular flows. (English) Zbl 1184.35256 J. Math. Anal. Appl. 349, No. 2, 583-595 (2009). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35Q31 35D30 76D03 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Math. Anal. Appl. 349, No. 2, 583--595 (2009; Zbl 1184.35256) Full Text: DOI arXiv
Shvydkoy, Roman; Friedlander, Susan The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity. (English) Zbl 1140.35550 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 4, 713-724 (2008). MSC: 35Q30 76D05 76M30 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{S. Friedlander}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 4, 713--724 (2008; Zbl 1140.35550) Full Text: DOI arXiv EuDML
Cheskidov, A.; Constantin, P.; Friedlander, S.; Shvydkoy, R. Energy conservation and Onsager’s conjecture for the Euler equations. (English) Zbl 1138.76020 Nonlinearity 21, No. 6, 1233-1252 (2008). MSC: 76B03 35Q35 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., Nonlinearity 21, No. 6, 1233--1252 (2008; Zbl 1138.76020) Full Text: DOI arXiv
Friedlander, Susan; Pavlović, Nataša; Shvydkoy, Roman Nonlinear instability for the Navier-Stokes equations. (English) Zbl 1233.35155 Commun. Math. Phys. 264, No. 2, 335-347 (2006). MSC: 35Q30 76D05 76E30 PDFBibTeX XMLCite \textit{S. Friedlander} et al., Commun. Math. Phys. 264, No. 2, 335--347 (2006; Zbl 1233.35155) Full Text: DOI arXiv
Shvydkoy, Roman The essential spectrum of advective equations. (English) Zbl 1121.76027 Commun. Math. Phys. 265, No. 2, 507-545 (2006). MSC: 76E30 35Q35 PDFBibTeX XMLCite \textit{R. Shvydkoy}, Commun. Math. Phys. 265, No. 2, 507--545 (2006; Zbl 1121.76027) Full Text: DOI arXiv
Shvydkoy, Roman Cocycles and Mañe sequences with an application to ideal fluids. (English) Zbl 1104.37003 J. Differ. Equations 229, No. 1, 49-62 (2006). MSC: 37A20 37N10 35Q05 34D09 76E20 76B99 PDFBibTeX XMLCite \textit{R. Shvydkoy}, J. Differ. Equations 229, No. 1, 49--62 (2006; Zbl 1104.37003) Full Text: DOI arXiv
Shvydkoy, Roman; Friedlander, Susan On recent developments in the spectral problem for the linearized Euler equation. (English) Zbl 1221.35303 Chen, Gui-Qiang (ed.) et al., Nonlinear partial differential equations and related analysis. The Emphasis Year 2002–2003 program, Evanston, IL, USA, September 2002–July 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3533-5/pbk). Contemporary Mathematics 371, 271-295 (2005). MSC: 35Q35 76B03 76E09 76E20 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{S. Friedlander}, Contemp. Math. 371, 271--295 (2005; Zbl 1221.35303)
Shvydkoy, Roman; Latushkin, Yuri Essential spectrum of the linearized 2D Euler equation and Lyapunov-Oseledets exponents. (English) Zbl 1329.76028 J. Math. Fluid Mech. 7, No. 2, 164-178 (2005). MSC: 76B03 37N10 37D45 76E99 35Q31 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{Y. Latushkin}, J. Math. Fluid Mech. 7, No. 2, 164--178 (2005; Zbl 1329.76028) Full Text: DOI arXiv
Friedlander, Susan; Shvydkoy, Roman The unstable spectrum of the surface quasi-geostrophic equation. (English) Zbl 1064.76046 J. Math. Fluid Mech. 7, Suppl. 1, S81-S93 (2005). MSC: 76E20 35P05 35Q35 76U05 86A05 PDFBibTeX XMLCite \textit{S. Friedlander} and \textit{R. Shvydkoy}, J. Math. Fluid Mech. 7, S81--S93 (2005; Zbl 1064.76046) Full Text: DOI
Shvydkoy, Roman; Vishik, Misha On spectrum of the linearized 3D Euler equation. (English) Zbl 1074.76027 Dyn. Partial Differ. Equ. 1, No. 1, 49-63 (2004). MSC: 76E99 76B03 35Q35 35P15 PDFBibTeX XMLCite \textit{R. Shvydkoy} and \textit{M. Vishik}, Dyn. Partial Differ. Equ. 1, No. 1, 49--63 (2004; Zbl 1074.76027) Full Text: DOI
Li, Y. Charles; Shvidkoy, Roman Isospectral theory of Euler equations. (English) Zbl 1060.35101 J. Math. Anal. Appl. 292, No. 1, 311-315 (2004). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35Q05 76B03 35Q30 PDFBibTeX XMLCite \textit{Y. C. Li} and \textit{R. Shvidkoy}, J. Math. Anal. Appl. 292, No. 1, 311--315 (2004; Zbl 1060.35101) Full Text: DOI arXiv
Bátkai, A.; Fašanga, E.; Shvidkoy, R. Hyperbolicity of delay equations via Fourier multipliers. (English) Zbl 1050.35120 Acta Sci. Math. 69, No. 1-2, 131-145 (2003). Reviewer: Josef Diblík (Brno) MSC: 35R10 42B15 35B35 PDFBibTeX XMLCite \textit{A. Bátkai} et al., Acta Sci. Math. 69, No. 1--2, 131--145 (2003; Zbl 1050.35120)
Shvidkoy, Roman; Latushkin, Yuri The essential spectrum of the lienarized 2D Euler operator is a vertical band. (English) Zbl 1109.76311 Karpeshina, Yulia (ed.) et al., Advances in differential equations and mathematical physics. Proceedings of the 9th UAB international conference, University of Alabama, Birmingham, AL, USA, March 26–30, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3296-4). Contemp. Math. 327, 299-304 (2003). MSC: 76B99 35P05 35Q35 37N10 76E05 PDFBibTeX XMLCite \textit{R. Shvidkoy} and \textit{Y. Latushkin}, Contemp. Math. 327, 299--304 (2003; Zbl 1109.76311) Full Text: arXiv