Reading seminar: Navier-Stokes equations

Abstract

This is not a regular lecture, but rather a reading seminar, in which students and postdocs will be asked to give lectures on some selected papers about the Navier-Stokes equations.
The Navier-Stokes equations (suitably coupled with other supplemental equations) model in a quite accurately way the motion of viscous fluids under several conditions. These equations have been studied since a long time, but still the main basic questions, such as the existence of solutions for all times, remain open. The reasons for this lack of understanding have to be found in the structure of the equations, which are nonlinear and involve a certain Lagrange multiplier, the pressure.
The aim of the seminar is to give an introduction to the subject, by presenting and discussing some of the fundamental papers on this topic. In particular, the following results (but not only!) will be discussed:

  • existence of Leray's weak solutions;
  • Serrin's regularity conditions;
  • Caffarelli-Kohn-Niremberg's partial regularity;
  • Recent results by Constantin, Sverak and others on suitable regularity criteria.
06.03.2017, 10:18