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arXiv · 1908.00055

Well-posedness for a Whitham-Boussinesq system with surface tension

Evgueni Dinvay
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Abstract

We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. The system can be seen as a weak nonlocal dispersive perturbation of the shallow water system. The proof of well-posedness relies on energy estimates. However, due to the symmetry lack of the nonlinear part, in order to close the a priori estimates one has to modify the traditional energy norm in use. Hamiltonian conservation provides with global well-posedness at least for small initial data in the one dimensional settings.

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Evgueni Dinvay. 2019-07-31. Well-posedness for a Whitham-Boussinesq system with surface tension. https://doi.org/10.1007/s11040-020-09339-1

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