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A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid
1. | Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
2. | Department of Mathematics, University of Southern California, Los Angeles, CA 91107, USA |
We derive a priori estimates for the compressible free-boundary Euler equations with surface tension in three spatial dimensions in the case of a liquid. These are estimates for local existence in Lagrangian coordinates when the initial velocity and initial density belong to H3, with an extra regularity condition on the moving boundary, thus lowering the regularity of the initial data. Our methods are direct and involve two key elements: the boundary regularity provided by the mean curvature and a new compressible Cauchy invariance.
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