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

Kalisch, Henrik; Pilod, Didier

doi:10.1090/proc/14397

On the local well-posedness for a full-dispersion Boussinesq system with surface tension
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by Henrik Kalisch and Didier Pilod

Proc. Amer. Math. Soc. 147 (2019), 2545-2559

DOI: https://doi.org/10.1090/proc/14397

Published electronically: February 14, 2019

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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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