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arXiv · 1805.04372

On the local well-posedness for a full dispersion Boussinesq system with surface tension

Henrik Kalisch·Didier Pilod
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Abstract

In this note, we prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions. Those systems can be seen as a weak nonlocal dispersive perturbation of the shallow-water system. Our method of proof relies on energy estimates and a compactness argument. However, due to the lack of symmetry of the nonlinear part, those traditional methods have to be supplemented with the use of a modified energy in order to close the a priori estimates.

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Henrik Kalisch, Didier Pilod. 2018-05-11. On the local well-posedness for a full dispersion Boussinesq system with surface tension. https://arxiv.org/abs/1805.04372

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