Alexey Cheskidov
Professor and Director of Graduate Studies
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
Erdös number: 3
Editorial board member
Discrete and Continuous Dynamical Systems  Series S
Letters in Mathematical Sciences
Teaching: Math 417, Math 580
UIC Workshop on Nonlinear Waves
Research Papers:
 Stationary and discontinuous weak solutions of the NavierStokes equations (with X. Luo). Submitted, arXiv:1901.07485, PDFrevised, (2019).
 Local estimates of Hölder exponents in turbulent vector fields (with Florian Nguyen, JeanPhilippe Laval, Pierre Kestener, Roman Shvydkoy, Bérengère Dubrulle). Submitted, hal02013816, (2019).
 Energy equality for the NavierStokes equations in weakintime Onsager spaces (with X. Luo). Submitted, arXiv:1802.05785, (2018).
 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 L2 (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
 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, to appear, (2017). arXiv:1510.00379
 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.
 On the determining wavenumber for the nonautonomous subcritical SQG equation (with M. Dai),
arXiv:1508.07943, (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.

Regularizing effect of the forward energy cascade in the inviscid dyadic model (with K. Zaya), AMS Proceedings,
to appear, (2014).

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]
Talks:
 Workshop "Mathematical Aspects of Hydrodynamics'', Mathematisches Forschungsinstitut Oberwolfach,
OberwolfachWalke, Germany, August 9th15th, 2015.
 Minisymposium ``Fluid Dynamics", EquaDiff conference, Lyon, France, July 610, 2015.
 Nonlinear Partial Differential Equations seminar, Texas A&M University, Feb 24, 2015.
 Workshop ``Blowup for the equations of Fluid Dynamics and Renormalization Group methods'', GSSI, L'Aquila, Italy,
Agust 1829, 2014.
 Analysis of Fluids and Related Topics seminar, Princeton University, May 8, 2014.
 CAMP/Nonlinear PDE seminar, University of Chicago, March 12, 2014.
 Minisymposium "Analysis of Nonlinear Differential Equations Arising in Fluid Dynamics", SIAM conference on analysis of partial differential equations, Orlando, FL, December 710, 2013.
 Mathematics and Applications seminar, University of Sussex, UK, September 29, 2013.
 Special section ``Mathematics of Fluid Mechanics: from Turbulence to Free Boundaries'',
Mathematical Congress of the Americas, Guanajuato, Mexico, August 59, 2013.
 Summer school and workshop "Recent Advances in PDEs and Fluids", Stanford University,
August 518, 2013.
 Computational and Applied Mathematics Colloquium, Penn State, April 20, 2013.
 Conference "The NavierStokes in Venice", Venice, Italy, April 812, 2013.
 "Mathematical Aspects of Hydrodynamics", Oberwolfach Workshop, Mathematisches Forschungsinstitut Oberwolfach,
OberwolfachWalke, Germany, August 12th18th, 2012.
 Special Sessions ``Infinite Dimensional Dynamics and Applications'' and ``Recent Developments on Turbulence'', the 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Orlando, Florida, USA July 15, 2012.
 PDE Seminar, University of Minnesota, Minneapolis, April 4, 2012.
 "Incompressible Fluids, Turbulence and Mixing, In honor of Peter Constantins 60th birthday", Carnegie Mellon University, October 1316, 2011.
 PDE and Geometric Analysis Seminar, University of Wisconsin, Madison, April 11, 2011.
 Interdisciplinary Session on Deterministic and Stochastic Partial Differential Equations, Notre Dame University, Notre Dame, IN,
November 57, 2010.

Harmonic Analysis and Differential Equations seminar, University of
Illinois at UrbanaChampaign, September 21, 2010.

Workshop on Partial Differential Equations and Fluid Mechanics, Warwick, UK, July 59, 2010.

Special Session on Harmonic Analysis and Partial Differential Equations, AMS meeting, Waco, TX, October 1618, 2009.

Minisymposium "Recent Mathematical Advances in Fluid Models  Geophysical, Physiological, and Other Applications",
SIAM Conference on Applications of Dynamical Systems,
Snowbird, UT, May 1721, 2009.

Special Session on Nonlinear Partial Differential Equations, AMS meeting, San Francisco, CA, April 2526, 2009.
 Special section "Nonlinear Partial Differential Equations and Applications" at the AMS meeting, Urbana, IL, March 27, 2009.
 Shanks workshop ``Dynamics of interfaced and structures in fluid flows'', Vanderbilt University, October 1819, 2008.
 Special session on
Recent Advances in Classical and Geophysical Fluid Dynamics,
AMS Spring Central Section Meeting,
Bloomington, IN, April 56, 2008.

AIMS' Seventh International Conference on Dynamical Systems, Differential
Equations and Applications, Arlington, TX, May 1821, 2008.
 Special session on Nonlinear Partial Differential Equations and Applications
AMS 2007 Fall Southeastern Meeting,
Murfreesboro, TN, November 34, 2007.
 Special session Recent Developments in 2D Turbulence,
AMS Western Sectional Meeting, Albuquerque, NM Oct. 1314, 2007.
 Special session on the Euler and NavierStokes Equations,
AMS Fall Central Section Meeting,
DePaul University, Chicago, October 56th 2007.
 Analysis seminar, University of Southern California, September 20, 2007.
 Computational & Applied Mathematics Seminar, Purdue University, September 7, 2007.
 PDE/Applied Mathematics Seminar, Indiana University, Bloomington, September 3, 2007.
 Applied Mathematics and PDE seminar, University of Wisconsin, Madison, April 13, 2007.
 Special section on Theoretical and Numerical Issues in Fluid Dynamics, AMS Central Section Meeting,
March 1617, 2007.
 Mathematics and Applications Seminar, University of Illinois, Chicago, April 24, 2006.
 Minisimposium Analysis of the NavierStokes Equations and Related Models,
SIAM Conference on Analysis of Partial Differential Equations,
Boston, MA, July 1012, 2006.
 Minisimposium
Lyapunov Exponents and Stability Spectrum for Infinite Dimensional
Dynamical Systems,
SIAM Conference on Applications of Dynamical Systems,
Snowbird, UT, May 2226, 2005.
 Special section on
Recent Advances in Mathematical and Numerical
Studies of Fluid Dynamics,
Fifth International Conference on Dynamical Systems and Differential
Equations,
Pomona, CA, June 1619, 2004.
 Special section on
Recent Advances in the Mathematical Analysis of Geophysical
and Hydrodynamical Models,
2004 Spring Western Section Meeting, Los Angeles, CA, April 34, 2004.
 Geometrical mechanics and turbulence modeling:
Reduced Dimensional Modeling Workshop,
Center for Nonlinear Studies,
Los Alamos National Laboratory, Santa Fe, NM, December 57, 2003.
 Minisimposium Asymptotic Analysis of Certain Geophysical
and Hydrodynamic Flows,
SIAM Conference on Applications of Dynamical Systems,
Snowbird, UT, May 2731, 2003.
 Geometrical mechanics and turbulence modeling:
Reduced Dimensional Modeling Workshop, Center for Nonlinear Studies,
Los Alamos National Laboratory, November 79, 2002.
 Special section on Mathematical fluid dynamics,
Fourth International Conference on Dynamical Systems and Differential
Equations,
University of North Carolina, Wilmington, May 2427, 2002.

Computational and Applied Mathematics seminar,
University of California, Irvine, January 11, 2002.
 Special section on Recent developments in
analysis and numerics of fluid problems,
Joint Mathematics Meetings, San Diego, January 69, 2002.
 Reduced Dimensional Modeling workshop, Center for Nonlinear
Studies,
Los Alamos National Laboratory, November 89, 2001.
 Partial Differential Equations in Fluid Dynamics seminar,
Texas A&M University, April 24, 2001.

Third International Conference on Dynamical Systems and Differential Equations,
Kennesaw State University, May 21, 2000.