EVENT DETAILS AND ABSTRACT

Title: Dynamics of Singularity Surfaces for Compressible, Viscous Flows in Multidimension
Speaker: Professor David Hoff
Speaker Info: Indiana University
Brief Description:
Special Note:
Abstract:

I'll prove the existence of solutions of the Navier-Stokes equations of compressible, barotropic flow which are piecewise smooth. These solutions exhibit discontinuities in pressure and velocity gradient across hypersurfaces which are convected with the fluid, exactly as predicted by elementary considerations based on the Rankine-Hugoniot conditons. The strengths of discontinuities decay exponentially in time, more rapidly for smaller viscosity. An interesting feature of the analysis is some rather nonstandard elliptic theory in which the regularity of the discontinuity surface is coupled to the tangential regularity of the velocity field.