Vladimir Sverak's HomepageContact InfoVincent Hall 2366126251899 email: sverak"at"math.umn.edu Office HoursMonday 2:20  3:35, Wednesday 2:20  3:35 or by appointmentResearch InterestsPartial Differential EquationsTeachingFall 2014: Functional Analysis, Math 8801Materials from selected previous coursesIntroduction to Ordinary Differential Equations, Math 5525, Textbook , Course MaterialsSelected 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 PublicationsThe 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 NavierStokes equations locally illposed in the natural energy space? (with H. Jia) On Inviscid Limits for the Stochastic NavierStokes Equations and Related Models (with N. GlattHoltz and V. Vicol) Rescalings at possible singularities of NavierStokes equations in half space (with G. Seregin) On the Cauchy problem for axisymmetric vortex rings (with H. Feng) Localinspace estimates near initial time for weak solutions of the NavierStokes equations and forward selfsimilar solutions (with H. Jia) On scaleinvariant solutions of the NavierStokes equations (with H. Jia), Proceedings of the 6th ECM, Krakow Minimal $L^3$initial data for potential NavierStokes singularities (with H. Jia) Liouville theorems in unbounded domains for the timedependent Stokes system (with H. Jia and G. Seregin) Local structure of the set of steadystate solutions to the 2d incompressible Euler's equations (with A. Choffrut) Backward uniqueness for the heat equations in cones (with Lu Li) On divergencefree drifts (with L. Silvestre, G. Seregin, and A. Zlatos) PDE aspects of the NavierStokes equations Minimal initial data for potential NavierStokes singularities (with W. Rusin) On Type I singularities of the local axisymmetric solutions of the NavierStokes equations (with G. Seregin) On the largedistance asymptotics of steady state solutions of the NavierStokes equations in 3D exterior domains (with A. Korolev) Liouville theorems for the NavierStokes 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 NavierStokes Equations Parabolic systems with nowhere smooth solutions (with S. Mueller and M. Rieger), Arch. Ration. Mech. Anal. 177 (2005), no. 1, 120. $L\sb {3,\infty}$solutions of NavierStokes equations and backward uniqueness (with L. Escauriaza and G. Seregin), Uspekhi Mat. Nauk 58, no. 2 (350), 344; Convex integration for Lipschitz mappings and counterexamples to regularity (with S. Mueller), Ann. of Math. (2) 157 (2003), no. 3, 715742. LinksPDE seminar
