Alexey Cheskidov

Research Papers:

• Dissipation anomaly and anomalous dissipation in incompressible fluid flows, arXiv:2311.04182, (2024).
• L^2-critical nonuniqueness for the 2D Navier-Stokes equations (with X. Luo), Annals of PDE 9, 13,(2023).
• Sharp nonuniqueness for the Navier-Stokes equations (with X. Luo), Inventiones mathematicae, 229, 987--1054, (2022).
• Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions (with X. Luo), Analysis and PDE, to appear, arXiv:2204.08950, (2022).
• Gaining two derivatives on a singular force in the 2D Navier-Stokes Equations (with L. Kavlie), Journar of Differential Equations, 341, 422--437 (2022).
• Volumetric theory of intermittency in fully developed turbulence (with R. Shvydkoy), Archive for Rational Mechanics and Analysis 247, 45 (2023), PDF, arXiv:2203.11060.
• The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence (with M. Dai), PDF, arXiv:2112.11606, (2022).
• Dyadic models for fluid equations: a survey (with M. Dai and S. Friedlander), Journal of Mathematical Fluid Mechanics, to appear, arXiv:2209.10203, (2022).
• Nonuniqueness of weak solutions for the transport equation at critical space regularity (with X. Luo). Annals of PDE 7, 2 (2021), arxiv:2004.09538.
• Anomalous dissipation, anomalous work, and energy balance for smooth solutions of the Navier-Stokes equations (with X. Luo). SIAM J. Math. Anal., 53(4), 3856-3887, arXiv:1910.07485, (2021).
• The computation of wandering points on the global attractor by means of symmetry-breaking perturbations (with E. Olson and B. Smith). Pure and Applied Functional Analysis, dedicated to Ciprian Foias (2021).
• Susan Friedlander's contributions in mathematical fluid dynamics (with N. Glatt-Holtz, N. Pavlovic, R. Shvydkoy, & V. Vicol). Notices of the American Mathematical Society, 68(3), 331-343 (2021).
• Discontinuity of weak solutions to the 3D Navier-Stokes and MHD equations in critical and supercritical spaces (with M. Dai). Journal of Mathematical Analysis and Applications, 481(2), (2020).
• Energy equality for the Navier-Stokes equations in weak-in-time Onsager spaces (with X. Luo). Nonlinearity, 33(4), 1388-1403, (2020), arXiv:1802.05785.
• On the determining wavenumber for the nonautonomous subcritical SQG equation (with M. Dai), Journal of Dynamics and Differential Equations, 32(3), 1511-1525, (2020), arXiv:1508.07943.
• Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations (with M. Dai). Proceedings of the Royal Society of Edinburgh: Section A, 149, 429-446 (2019). arXiv:1510.00379.
• Local estimates of Holder exponents in turbulent vector fields (with Florian Nguyen, Jean-Philippe Laval, Pierre Kestener, Roman Shvydkoy, Bérengère Dubrulle). Phys. Rev. E 99, 053114, (2019), hal-02013816.
• Determining modes for the surface quasi-geostrophic equation (with M. Dai). Physica D, Vol. 376-377, Special Issue: Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics, 204-215, (2018). arXiv:1507.01075
• The existence of a global attractor for the forced critical surface quasi-geostrophic equation in L^2 (with M. Dai). J. Math. Fluid. Mech., 20, 213-22, (2018), arXiv:1402.4801.
• Determining modes for the 3D Navier-Stokes equations (with M. Dai and L. Kavlie). Physica D, 374: 1–9, (2018), arXiv:1507.05908.
• Global attractor for a Ginzburg-Landau type model of rotating Bose-Einstein condensates (with D. Marahrens, and C. Sparber). Dynamics of PDE, 14, 5–32, (2017), arXiv:1506.04706.
• Energy conservation in two-dimensional incompressible ideal fluids (with M. C. Lopes Filho, H. J. Nussenzveig Lopes, and R. Shvydkoy). Communications in Mathematical Physics, 348: 129-143, (2016).
• Lower bounds of potential blow-up solutions of the three-dimensional Navier-StokesEquations in H^{3/2} (with K. Zaya), Journal of Mathematical Physics, 0.1063/1.4941035 (2016). arXiv:1503.01784.
• Regularizing effect of the forward energy cascade in the inviscid dyadic model (with K. Zaya), Proc. Amer. Math. Soc. 144, 73--85, (2016).
• Regularity criteria for the 3D Navier-Stokes and MHD equations (with M. Dai), arXiv:1507.06611, (2015).
• Degenerate pullback attractors for the 3D Navier-Stokes equations (with L. Kavlie), J. Math. Fluid Mech. 17 (2015), 411-421. arXiv:1403.6200, (2015).
• Norm inflation for generalized magneto-hydrodynamic system (with M. Dai) Nonlinearity 28 (2015) 129, arXiv:1402.1897.
• Pullback attractors for generalized evolutionary system (with L. Kavlie) DCDS-B 20 (2015), 749--779, arXiv:1310.4917.
• Norm inflation for generalized Navier-Stokes Equations (with M. Dai), Indiana Univ. Math. J. 63 (2014), 869-884, arXiv:1212.3801
• Uniform global attractors for the nonautonomous 3D Navier-Stokes equations (with S. Lu), Advances in Mathematics 267 (2014), 277-306, [sciencedirect]
• Euler equations and turbulence: analytical approach to intermittency (with R. Shvydkoy), SIAM J. Math. Anal., 46(1), 353-374 (2014), arXiv:1202.1460v1
• A unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov's dissipation range (with R. Shvydkoy), J. Math. Fluid Mech., DOI 10.1007 (2014), arXiv:1102.1944, [PDF]
• Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces (with R. Shvydkoy), J. Math. Phys. 53, 115620 (2012) [JMP, PDF]
• A Continuous Model for Turbulent Energy Cascade (with S. Friedlander and R. Shvydkoy), Mathematical aspects of fluid mechanics, London mathematical society lecture note series (No. 402), Cambridge University Press, 2012.
• ll-posedness of basic equations of fluid dynamics in Besov spaces (with R. Shvydkoy), AMS Proceedings 138 (2010), 1059-1067, [PDF]
• The regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$ (with R. Shvydkoy), Archive for Rational Mechanics and Analysis, 195 (2010), 159-169, [PDF]
• An inviscid dyadic model of turbulence: the global attractor (with S. Friedlander and N. Pavlovic), DCDS-A, 26 (2010), 781-794. [PDF]
• On the energy equality for weak solutions of the 3D Navier-Stokes equations (with S. Friedlander and R. Shvydkoy), Advances In Mathematical Fluid Mechanics: Dedicated To Giovanni Paolo Galdi On The Occasion Of His 60th Birthday, Springer, 2010, [PDF]
• Global attractors of evolutionary systems, J. Dyn. Diff. Equat. 21 (2009), 249-268. [JDDE, PDF]
• The existence and the structure of uniform global attractors for nonautonomous reaction-diffusion systems without uniqueness (with S. Lu), Discrete and Continuous Dynamical Systems - S 2 (2009), 55-66.
• The vanishing viscosity limit for a dyadic model (with S. Friedlander), Physica D 238 (2009) 783-787.
• On a relation between Lyapunov exponents and the radius of analyticity (with E. S. Van Vleck and M. S. Jolly), Indiana Univ. Math. J. 57 (2008), 2663-2680.
• Energy conservation and Onsager's conjecture for the Euler equations (with P. Constantin, S. Friedlander, and R. Shvydkoy), Nonlinearity 21 (2008), 1233-1252 [, PDF-revised]
• Blow-up in finite time for the dyadic model of the Navier-Stokes equations, AMS Tran., 360 (2008), 5101-5120. [PDF]
• Leray-alpha model and transition to turbulence in rough-wall boundary layers (with D. Ma), submitted, arXiv:physics/0611001 [PDF]
• Energy dissipation in fractal-forced flow (with C. Doering and N. Petrov), J. Math. Phys. 48, 065208 (2007). [JMP, PDF]
• An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture (With S. Friedlander and N. Pavlovic), J. Math. Phys. 48, 065503 (2007). [JMP, PDF]
• On global attractors of the 3D Navier-Stokes equations (with C. Foias), Journal of Differential Equations 231 (2006), 714-754. [ScienceDirect, PDF]
• Theoretical skin-friction law in a turbulent boundary layer, Physics Letters A 341 (2005), 487-494. [ScienceDirect, PDF, or PostScript]
• On a Leray-alpha model of turbulence (with D. D. Holm, E. Olson, and E. S. Titi), Royal Society London, Proceedings, Series A 461 (2005), 1-21. [Royal Society, PDF]
• Boundary layer for the Navier-Stokes-alpha model of fluid turbulence, Archive for Rational Mechanics and Analysis 172 (2004), 333-362 [SpringerLink, PDF, or PostScript]
• Turbulent boundary layer equations, C. R. Acad. Sci. Paris, Ser. I 334 (2002), 423-427. [ScienceDirect, PDF, or PostScript]
• On the Non-Homogeneous Stationary Kuramoto-Sivashinsky Equation (with C. Foias), Physica D 154 (2001), 1-14.
  [ScienceDirect, PDF, or PostScript]
• Appendix in Evaluating the Dimension of an Inertial Manifold for the Kuramoto-Sivashinsky Equation by M.S. Jolly, R. Rosa, and R. Temam, Advances in Differential Equations 5 (2000), 31-66.
  [PDF, or PostScript]
• On finite groups with restrictions on centralizers (with V.A. Antonov and I.A. Tyurina), (Russian) Mat. Zametki 71 (2002), 483-495, translation in Mathematical Notes 71 (2002), 443-454. [SpringerLink]
• Groups with Small Centralizers (with V.A. Antonov and I.A. Tyurina) (Russian) Mat. Zametki 69 (2001), 643-655; translation in Mathematical Notes 69 (2001), 593-604. [SpringerLink]