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arXiv · 1708.00086

A priori estimates for the free-boundary Euler equations with surface tension in three dimensions

Marcelo M. Disconzi·Igor Kukavica
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Abstract

We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial velocity, which is rotational, belongs to $H^3$ and the trace of initial velocity on the free boundary to $H^{3.5}$, thus lowering the requirement on the regularity of initial data in the Lagrangian setting. Our methods are direct and involve three key elements: estimates for the pressure, the boundary regularity provided by the mean curvature, and the Cauchy invariance.

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Marcelo M. Disconzi, Igor Kukavica. 2017-07-31. A priori estimates for the free-boundary Euler equations with surface tension in three dimensions. https://doi.org/10.1088/1361-6544%2Fab0b0d

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