PDE Real Analysis Seminar The Lipschitz truncation method

2007-07-04 10:30 - 2007-07-04 11:30
Graduate School of Mathematical Sciences the University of Tokyo, Room #056
Professor Lars Diening (Universitat Freiburg)
We study the existence of weak solutions to the incompressible $p$-Navier Stokes equations. This system can be used to describe the flow of honey,ketchup, blood, suspensions, polymers, and glaciers. We are interested insmall values of $p$, where the method of monotone operators fails. We establish weak solutions by means of the Lipschitz truncation technique,where Sobolev Functions are approximated by Lipschitz functions in a specialway. We apply the technique also to electrorheological fluids, where theexponent $p$ depends on the electric field.