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Applied Math Seminar
A priori estimates for the free-boundary 3-D compressible Euler
equations in physical vacuum
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We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied. This is in collaboration with D. Coutand and H. Lindblad. |