University of Minnesota
Aerospace Engineering and Mechanics
Spring 2001 Seminar Series



On self-similar singular solutions of the incompressible Navier-Stokes equations and the Complex Ginzburg-Landau equations


Prof. Vladmir Sverak

School of Mathematics, University of Minnesota


Abstract


The topic of this talk is motivated by the open problem of regularity of solutions of the incompressible Navier-Stokes equations (NSE). It is well-known that, in three-dimensions, the non-linearity in the NSE is super-critical. This means that - unless some hidden and yet undiscovered restrictions on solutions are taken into account - the energy dissipation may by itself be insufficient to prevent a breakdown of solutions which are initially smooth. An example of a simpler PDE where one can study this phenomena is the Complex Ginzburg Landau Equation (CGL). The simplest conceivable singularities for both NSE and CGL which would be compatible with energy dissipation are the self-similar singularities. For the NSE, the question about the existence of such singularities was raised already in 1934 by J. Leray. During the last few years a significant progress has been made in our understanding of these questions, and in the talk I will explain these new results.

Friday, January 26, 2001
209 Akerman Hall
2:30-3:30 p.m.


Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.