PDE Real Analysis Seminar Maximal Regularity for Mixed Order Systems

2008-03-19 10:30 - 2008-03-19 11:30
Graduate School of Mathematical Sciences the University of Tokyo, Room #056
Juergen Saal (University of Konstanz)
In classical boundary value problems the related symbols are homogeneous in space and time. This allows for the application of a standard compactness argument in order to obtain the important maximal regularity. However, quasilinear systems arising e.g. from free boundary problems are in general of mixed order. In other words the related symbols are of intricate structure and in particular highly inhomogeneous. Therefore, the standard compactness argument fails. The purpose of this talk is to introduce the Newton polygon method, which gives a systematic approach to such mixed order systems and to demonstrate its strength by applications to the Stefan problem and a free boundary problem for the Navier-Stokes equations.