DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, April 25 Padelford C-36 3:45 PM

Regularity of Stokes-like elliptic system

David Maxwell (UW)

This talk concerns a class of nonlinear degenerate elliptic systems associated with the Stokes system. These equations have applications to certain non-Newtonian fluids and also have theoretical uses. Unlike the Navier-Stokes equations in three dimensions, we can prove that the corresponding evolution equations for many of these systems have unique weak solutions. However, the regularity theory of Stokes-like systems is currently unsatisfactory, especially in domains with boundaries. I’ll present an interior regularity result for bounded domains and discuss gaps in the overall theory.