Alexey Cheskidov
Professor
Department of Mathematics
University of Illinois at Chicago
MSCS (m/c 249), 851 S Morgan St, Chicago, IL 606077045
Email: acheskid (at) uic.edu
CV:
[PDF]
Area of Research: Nonlinear PDE, Fluid Dynamics, and InfiniteDimensional Dynamical Systems.
Thesis Advisor:
Ciprian Foias
Research Papers:
 Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions (with X. Luo), arXiv:2204.08950, (2022).
 Sharp nonuniqueness for the NavierStokes equations (with X. Luo), Inventiones mathematicae, to appear, arXiv:2009.06596, (2022).
 Volumetric theory of intermittency in fully developed turbulence (with R. Shvydkoy), PDF, arXiv:2203.11060, (2022).
 The number of degrees of freedom for the 2D NavierStokes equation: a connection with Kraichnan's theory of turbulence (with M. Dai), PDF, arXiv:2112.11606 , (2022).
 L^2critical nonuniqueness for the 2D NavierStokes equations (with X. Luo), PDF, arXiv:2105.12117, (2021).
 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 NavierStokes equations (with X. Luo). SIAM J. Math. Anal., 53(4), 38563887, arXiv:1910.07485, (2021).
 The computation of wandering points on the global attractor by means of symmetrybreaking 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. GlattHoltz, N. Pavlovic, R. Shvydkoy, & V. Vicol). Notices of the American Mathematical Society, 68(3), 331343 (2021).
 Discontinuity of weak solutions to the 3D NavierStokes and MHD equations in critical and supercritical spaces (with M. Dai). Journal of Mathematical Analysis and Applications, 481(2), (2020).
 Energy equality for the NavierStokes equations in weakintime Onsager spaces (with X. Luo). Nonlinearity, 33(4), 13881403, (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), 15111525, (2020),
arXiv:1508.07943.
 Kolmogorov's dissipation number and the number of degrees of freedom for the 3D NavierStokes equations (with M. Dai). Proceedings of the Royal Society of Edinburgh: Section A, 149, 429446 (2019). arXiv:1510.00379.
 Local estimates of Holder exponents in turbulent vector fields (with Florian Nguyen, JeanPhilippe Laval, Pierre Kestener, Roman Shvydkoy, Bérengère Dubrulle). Phys. Rev. E 99, 053114, (2019), hal02013816.
 Determining modes for the surface quasigeostrophic equation (with M. Dai). Physica D, Vol. 376377, Special Issue: Nonlinear Partial Differential Equations in Mathematical Fluid Dynamics, 204215, (2018). arXiv:1507.01075
 The existence of a global attractor for the forced critical surface quasigeostrophic equation in L^2 (with M. Dai). J. Math. Fluid. Mech., 20, 21322, (2018), arXiv:1402.4801.
 Determining modes for the 3D NavierStokes equations (with M. Dai and L. Kavlie). Physica D, 374: 1–9, (2018), arXiv:1507.05908.
 Global attractor for a GinzburgLandau type model of rotating BoseEinstein condensates (with D. Marahrens, and C. Sparber). Dynamics of PDE, 14, 5–32, (2017), arXiv:1506.04706.
 Energy conservation in twodimensional incompressible ideal fluids (with M. C. Lopes Filho, H. J. Nussenzveig Lopes, and R. Shvydkoy). Communications in Mathematical Physics, 348: 129143, (2016).
 Lower bounds of potential blowup solutions of the threedimensional NavierStokesEquations 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, 7385, (2016).
 Regularity criteria for the 3D NavierStokes and MHD equations (with M. Dai),
arXiv:1507.06611, (2015).
 Gaining two derivatives on a singular force in the 2D NavierStokes equations (with L. Kalvie),
arXiv:1502.05060, (2015)

Degenerate pullback attractors for the 3D NavierStokes equations (with L. Kavlie),
J. Math. Fluid Mech. 17 (2015), 411421. arXiv:1403.6200, (2015).

Norm inflation for generalized magnetohydrodynamic system (with M. Dai) Nonlinearity 28 (2015) 129,
arXiv:1402.1897.

Pullback attractors for generalized evolutionary system (with L. Kavlie) DCDSB 20 (2015), 749779, arXiv:1310.4917.

Norm inflation for generalized NavierStokes Equations (with M. Dai), Indiana Univ. Math. J. 63 (2014), 869884,
arXiv:1212.3801

Uniform global attractors for the nonautonomous 3D NavierStokes equations (with S. Lu), Advances in Mathematics 267 (2014), 277306,
[sciencedirect]

Euler equations and turbulence: analytical approach to intermittency (with R. Shvydkoy),SIAM J. Math. Anal., 46(1), 353374 (2014),
arXiv:1202.1460v1

A unified approach to regularity problems for the 3D NavierStokes 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]
 Illposedness for subcritical hyperdissipative NavierStokes 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.

llposedness of basic equations of fluid dynamics in Besov spaces (with R. Shvydkoy),
AMS Proceedings 138 (2010), 10591067,
[PDF]

The regularity of weak solutions of the 3D NavierStokes equations in $B^{1}_{\infty,\infty}$ (with R. Shvydkoy), Archive for Rational Mechanics and Analysis , 195 (2010), 159169, [PDF]
 An inviscid dyadic model of turbulence: the global attractor (with
S. Friedlander and N. Pavlovic), DCDSA, 26 (2010), 781794.
[PDF]

On the energy equality for weak solutions of the 3D NavierStokes 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]

An inviscid dyadic model of turbulence: the global attractor (with S. Friedlander and N. Pavlovic),
DCDSA 26 (2010), 781794.
 Global attractors of evolutionary systems, J. Dyn. Diff. Equat. 21 (2009), 249268.
[JDDE, PDF]

The existence and the structure of uniform global attractors for nonautonomous reactiondiffusion systems without uniqueness (with S. Lu), Discrete and Continuous Dynamical Systems  S 2 (2009), 5566.

The vanishing viscosity limit for a dyadic model (with S. Friedlander), Physica D 238 (2009) 783787.
 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), 26632680.

Energy conservation and Onsager's conjecture for the Euler equations (with P. Constantin, S. Friedlander, and R. Shvydkoy), Nonlinearity 21
(2008), 12331252
[, PDFrevised]
 Blowup in finite time for the dyadic model
of the NavierStokes equations, AMS Tran.,
360 (2008), 51015120.
[PDF]
 Lerayalpha model and transition to turbulence in roughwall boundary layers (with D. Ma), submitted,
arXiv:physics/0611001
[PDF]
 Energy dissipation in fractalforced 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
NavierStokes equations (with C. Foias), Journal of
Differential Equations 231 (2006), 714754.
[ScienceDirect, PDF]
 Theoretical skinfriction law in a turbulent boundary layer,
Physics Letters A 341 (2005), 487494.
[ScienceDirect, PDF, or
PostScript]
 On a Lerayalpha model of turbulence
(with D. D. Holm, E. Olson, and E. S. Titi),
Royal Society London, Proceedings, Series A 461 (2005), 121.
[Royal Society,
PDF]
 Boundary layer for the NavierStokesalpha
model of fluid turbulence,
Archive for Rational Mechanics and Analysis 172 (2004), 333362
[SpringerLink,
PDF, or
PostScript]
 Turbulent boundary layer equations,
C. R. Acad. Sci. Paris, Ser. I 334 (2002), 423427.
[ScienceDirect,
PDF, or
PostScript]
 On the NonHomogeneous Stationary KuramotoSivashinsky Equation
(with C. Foias), Physica D 154 (2001), 114.
[ScienceDirect,
PDF, or
PostScript]
 Appendix in Evaluating the Dimension of an Inertial Manifold for the
KuramotoSivashinsky Equation by M.S. Jolly, R. Rosa, and R. Temam,
Advances in Differential Equations 5 (2000), 3166.
[PDF, or
PostScript]
 On finite groups with restrictions on centralizers (with V.A. Antonov and I.A. Tyurina),
(Russian) Mat. Zametki 71 (2002), 483495,
translation in Mathematical Notes 71 (2002), 443454.
[SpringerLink]
 Groups with Small Centralizers (with V.A. Antonov and I.A. Tyurina) (Russian)
Mat. Zametki 69 (2001), 643655;
translation in Mathematical Notes 69 (2001),
593604.
[SpringerLink]