### 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

### Teaching

Fall 2014: Functional Analysis, Math 8801

### 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 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.