Vladimir Sverak's Homepage

Contact Info

Vincent Hall 236
e-mail: sverak"at"math.umn.edu

Office Hours

Monday 2:20 -- 3:35, Wednesday 2:20 - 3:35 or by appointment

Research Interests

Partial Differential Equations


Spring 2017: Topics in Continuum Mechanics, Math 8470

Materials from selected previous courses

Introduction to Ordinary Differential Equations, Math 5525, Textbook , Course Materials

Selected Topics in Fluid Mechanics (an introductory graduate course taught in 2011/2012), Course notes

Theory of PDE (an introductory graduate course taught in 2010/2011), Course notes

Recent Publications

The research has been supported in part by grants DMS 1101428 and DMS 1362467 from the National Science Foundation.
On global weak solutions to the Cauchy problem for the Navier-Stokes equations with large L3-initial data (with G. Seregin)
On 2d incompressible Euler equations with partial damping (with T. Elgindi and W. Hu)
Dynamics of geodesic flows with random forcing on Lie groups with left-invariant metrics (with W. Hu)
Remarks on the Cauchy problem for the axisymmetric Navier-Stokes equations (with Thierry Gallay)
On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations (with K. Choi, G. Luo, T. Hou, A. Kiselev, and Y. Yao)
Small scale creation for solutions of the incompressible two dimensional Euler equation (with A. Kiselev)
Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space? (with H. Jia)
On Inviscid Limits for the Stochastic Navier-Stokes Equations and Related Models (with N. Glatt-Holtz and V. Vicol)
Rescalings at possible singularities of Navier-Stokes equations in half space (with G. Seregin)
On the Cauchy problem for axi-symmetric vortex rings (with H. Feng)
Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions (with H. Jia)
On scale-invariant solutions of the Navier-Stokes equations (with H. Jia), Proceedings of the 6th ECM, Krakow
Minimal $L^3$-initial data for potential Navier-Stokes singularities (with H. Jia)
Liouville theorems in unbounded domains for the time-dependent Stokes system (with H. Jia and G. Seregin)
Local structure of the set of steady-state solutions to the 2d incompressible Euler's equations (with A. Choffrut)
Backward uniqueness for the heat equations in cones (with Lu Li)
On divergence-free drifts (with L. Silvestre, G. Seregin, and A. Zlatos)
PDE aspects of the Navier-Stokes equations
Minimal initial data for potential Navier-Stokes singularities (with W. Rusin)
On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations (with G. Seregin)
On the large-distance asymptotics of steady state solutions of the Navier-Stokes equations in 3D exterior domains (with A. Korolev)
Liouville theorems for the Navier-Stokes equations and applications (with G. Koch, N. Nadirashvili and G. Seregin)
Zeros of complex caloric functions and singularities of complex viscous Burgers equations (with P. Polacik)
On Landau's solutions of the Navier-Stokes Equations
Parabolic systems with nowhere smooth solutions (with S. Mueller and M. Rieger),
Arch. Ration. Mech. Anal. 177 (2005), no. 1, 1--20.
$L\sb {3,\infty}$-solutions of Navier-Stokes equations and backward uniqueness (with L. Escauriaza and G. Seregin),
Uspekhi Mat. Nauk 58, no. 2 (350), 3--44;
Convex integration for Lipschitz mappings and counterexamples to regularity (with S. Mueller),
Ann. of Math. (2) 157 (2003), no. 3, 715--742.


PDE seminar
School of Mathematics
Recent Arxiv PDE preprints

Last Modified Monday January 09, 2017
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