The viscous surface wave problem with generalized surface energies

Antoine Remond-Tiedrez; Ian Tice

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arXiv · 1806.07660

The viscous surface wave problem with generalized surface energies

Antoine Remond-Tiedrez·Ian Tice

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Abstract

We study a three-dimensional incompressible viscous fluid in a horizontally periodic domain with finite depth whose free boundary is the graph of a function. The fluid is subject to gravity and generalized forces arising from a surface energy. The surface energy incorporates both bending and surface tension effects. We prove that for initial conditions sufficiently close to equilibrium the problem is globally well-posed and solutions decay to equilibrium exponentially fast, in an appropriate norm. Our proof is centered around a nonlinear energy method that is coupled to careful estimates of the fully nonlinear surface energy.

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Antoine Remond-Tiedrez, Ian Tice. 2018-06-20. The viscous surface wave problem with generalized surface energies. https://arxiv.org/abs/1806.07660

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