2 mar 2005
Abstract.
Seminari di calcolo delle variazioni
when: Wednesday, March 2, at 5.30 pm
where: Dipartimento di Matematica, sala delle riunioni
speaker: Didier Smets (Paris VI and Centro E. De Giorgi)
title: The Navier-Stokes equation for viscous fluids : an introduction to the basic regularity results
abstract: We will try to present a self-contained introduction to some basic regularity results in the mathematical treatment of the Navier-Stokes equations. These include:
1) the local well-posedness in spaces of regular functions (a fixed point argument after some easy kernel estimates);
2) the global existence of weak solutions (after Jean Leray 1934 Acta paper);
3) the space-time size estimate on possible singularities (after Caffarelli-Kohn-Nirenberg 1984 CPAM paper);
4) (possibly) some recent results of Escauriaza-Seregin-Sverak on the blow-up of the spatial $L^3$-norm on a singularity.