Helge Kristian Jenssen
North Carolina State University, Raleigh
We prove the global existence of weak solutions of the Navier-Stokes equations of compressible and heat conductive (nonbarotropic) flow in three space dimensions with initial data and external forces which are large, discontinuous, and spherically or cylindrically symmetric. Large data results for general flow patterns seems beyond the reach of present techniques. Exploiting symmetry we combine one- and multi-dimensional techniques to obtain a priori bounds on density and temperature. We will discuss the possibility of vacuum states opening up at the origin and we will comment on recent attempts to make the equations more physical by considering non-constant transport coefficients (viscosity and heat conductivity). This is joint work with David Hoff (Indiana).