Vladimir Sverak's Homepage

Contact Info

Vincent Hall 236
612-625-1899
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

Courses

Spring 2014: Topics in PDE, Math 8590

Spring 2013: Introduction to Ordinary Differential Equations, Math 5525, Textbook , Course Materials

Fall 2011 / Spring 2012: Topics in Mathematical Physics, Math 8390/8391, Course notes

Fall 2010 / Spring 2011: Theory of PDE, Math 8583/8584, Course notes

Recent Publications

The research has been supported in part by grants DMS 0800908 and DMS 1101428 from the National Science Foundation.
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.

Links

PDE seminar
School of Mathematics
Recent Arxiv PDE preprints
MathSciNet

Last Modified Tuesday January 21, 2014
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