Alexey Cheskidov

Editorial board member Discrete and Continuous Dynamical Systems - Series S

Teaching: Math 580

Research Papers:

• Norm inflation for generalized Navier-Stokes Equations (with M. Dai), [PDF]
• Uniform global attractors for the nonautonomous 3D Navier-Stokes equations (with S. Lu), [PDF]
• Euler equations and turbulence: analytical approach to intermittency (with R. Shvydkoy), 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), arXiv:1102.1944, (2011), [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]
• An inviscid dyadic model of turbulence: the global attractor (with S. Friedlander and N. Pavlovic), DCDS-A 26 (2010), 781-794.
• 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]

Talks:

• 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 5-7, 2010.
• Harmonic Analysis and Differential Equations seminar, University of Illinois at Urbana-Champaign, September 21, 2010.
• Workshop on Partial Differential Equations and Fluid Mechanics, Warwick, UK, July 5--9, 2010.
• Special Session on Harmonic Analysis and Partial Differential Equations, AMS meeting, Waco, TX, October 16-18, 2009.
• Minisymposium "Recent Mathematical Advances in Fluid Models - Geophysical, Physiological, and Other Applications", SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 17-21, 2009.
• Special Session on Nonlinear Partial Differential Equations, AMS meeting, San Francisco, CA, April 25-26, 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 18-19, 2008.
• Special session on Recent Advances in Classical and Geophysical Fluid Dynamics,
  AMS Spring Central Section Meeting, Bloomington, IN, April 5-6, 2008.
  
• AIMS' Seventh International Conference on Dynamical Systems, Differential Equations and Applications, Arlington, TX, May 18-21, 2008.
  
• Special session on Nonlinear Partial Differential Equations and Applications
  AMS 2007 Fall Southeastern Meeting, Murfreesboro, TN, November 3-4, 2007.
  
• Special session Recent Developments in 2-D Turbulence,
  AMS Western Sectional Meeting, Albuquerque, NM Oct. 13-14, 2007.
  
• Special session on the Euler and Navier-Stokes Equations,
  AMS Fall Central Section Meeting, DePaul University, Chicago, October 5-6th 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 16-17, 2007.
  
• Mathematics and Applications Seminar, University of Illinois, Chicago, April 24, 2006.
  
• Minisimposium Analysis of the Navier-Stokes Equations and Related Models,
  SIAM Conference on Analysis of Partial Differential Equations, Boston, MA, July 10-12, 2006.
  
• Minisimposium Lyapunov Exponents and Stability Spectrum for Infinite Dimensional Dynamical Systems,
  SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 22-26, 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 16--19, 2004.
  
• Special section on Recent Advances in the Mathematical Analysis of Geophysical and Hydrodynamical Models,
  2004 Spring Western Section Meeting, Los Angeles, CA, April 3-4, 2004.
  
• Geometrical mechanics and turbulence modeling:
  Reduced Dimensional Modeling Workshop, Center for Nonlinear Studies,
  Los Alamos National Laboratory, Santa Fe, NM, December 5--7, 2003.
  
• Minisimposium Asymptotic Analysis of Certain Geophysical and Hydrodynamic Flows,
  SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, May 27-31, 2003.
  
• Geometrical mechanics and turbulence modeling:
  Reduced Dimensional Modeling Workshop, Center for Nonlinear Studies,
  Los Alamos National Laboratory, November 7-9, 2002.
  
• Special section on Mathematical fluid dynamics,
  Fourth International Conference on Dynamical Systems and Differential Equations,
  University of North Carolina, Wilmington, May 24-27, 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 6-9, 2002.
  
• Reduced Dimensional Modeling workshop, Center for Nonlinear Studies,
  Los Alamos National Laboratory, November 8-9, 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.