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Outline

Organizers :

A.Miyachi (Tokyo Woman's Christian.U), Y.Giga (University of Tokyo/Hokkaido University)

Period :

July 4, 2007 (Wednesday) 10:30-11:30

Place :

Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Programme :

Professor Lars Diening (Universitat Freiburg)

TITLE:

The Lipschitz truncation method

ABSTRACT:

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 in small 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 special way. We apply the technique also to electrorheological fluids, where the exponent $p$ depends on the electric field.