Global well-posedness of the free-surface damped incompressible Euler equations with surface tension

We consider a layer of an incompressible inviscid fluid, bounded below by a fixed general bottom and above by a free moving boundary, in a horizontally periodic setting. The fluid dynamics is governed by the gravity-driven incompressible Euler equations with damping, and the effect of surface tension is included on the free surface. We prove that the problem is globally well-posed for the small initial data; moreover, the solution decays exponentially to the equilibrium.

Keywords

Euler, free boundary problems, damping, surface tension, global well-posedness

2010 Mathematics Subject Classification

35L60, 35Q35, 76B15

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This work was supported by the National Natural Science Foundation of China (No. 11771358).

Received 7 August 2018

Accepted 27 December 2018

Published 30 August 2019