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arXiv · 1911.01912

Well-posedness of a water wave model with viscous effects

Rafael Granero-Belinchón·Stefano Scrobogna
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Abstract

Starting from the paper by Dias, Dyachenko and Zakharov (\emph{Physics Letters A, 2008}) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with or without surface tension effects. This equation takes the form of a nonlocal fourth order wave equation and retains the main contributions to the dynamics of the free surface. Then, we prove the well-posedness in Sobolev spaces of such equation.

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Rafael Granero-Belinchón, Stefano Scrobogna. 2019-11-05. Well-posedness of a water wave model with viscous effects. https://arxiv.org/abs/1911.01912

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