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.