A Hyperbolic Free-Boundary Problem for 3D Compressible Euler Flow in Physical Vacuum

Monday, October 6, 2008 -
4:00pm to 6:00pm
We prove well-posedness for compressible flow with free-boundary in physical vacuum, modeled by the 3D compressible Euler equations. The vanishing of the density at the vacuum boundary induces degenerate hyperbolic equations that become characteristic, requiring a separate analysis of time, normal, and tangential derivatives to handle the manifest 1/2-derivative loss. Unfortunately, the methods for incompressible flow do not work for the degenerate compressible regime; a priori nonlinear estimates are obtained using the geometric structure of the Euler equations, and an existence theory is developed using a novel approximation scheme employing an artificial phase. The result is in collaboration with Coutand and Lindblad.
Steve Shkoller
University of California, Davis
Event Location: 
Fine Hall 110