A multidimensional piston problem for the Euler equations for compressible flow

Abstract

A multidimensional piston problem for the Euler equations for compressible isentropic flow is analyzed. The piston initially locates at the origin and experiences compressive and expansive motions with spherical symmetry. The initial singularity at the origin is one of the difficulties for this spherically symmetric piston problem. A local shock front solution for the compressive motion is constructed based on the linearization at an approximate solution and the Newton iteration. A global entropy solution for the piston problem is constructed by using a shock capturing approach and the method of compensated compactness.