A Hyperbolic FreeBoundary Problem for 3D Compressible Euler Flow in Physical Vacuum
A Hyperbolic FreeBoundary Problem for 3D Compressible Euler Flow in Physical Vacuum

Steve Shkoller, University of California, Davis
Fine Hall 110
We prove wellposedness for compressible flow with freeboundary 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 1/2derivative 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.