| Abstract: |
| In this talk, we consider a special class of the contact discontinuity in the full compressible Euler equations, namely the entropy wave, where the velocity is continuous across the interface while the density and the entropy can have jumps. By deriving the evolution equation of the interface in the Eulerian coordinates, we relate the Taylor sign condition to the hyperbolicity of this evolution equation, which yields a stability condition for the entropy waves. With the optimal regularity estimates of the interface, we can derive the a priori estimates without loss of regularity. |
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