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arXiv · 1708.00861

A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid

Marcelo M. Disconzi·Igor Kukavica
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Abstract

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 $H^3$, 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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Marcelo M. Disconzi, Igor Kukavica. 2017-08-02. A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid. https://doi.org/10.3934/eect.2019025

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