Well-Posedness for a Whitham-Boussinesq System with Surface Tension
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.
- Publication:
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Mathematical Physics, Analysis and Geometry
- Pub Date:
- May 2020
- DOI:
- 10.1007/s11040-020-09339-1
- arXiv:
- arXiv:1908.00055
- Bibcode:
- 2020MPAG...23...23D
- Keywords:
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- Water waves;
- Nonlinear dispersive equations;
- Well-posedness;
- Mathematics - Analysis of PDEs
- E-Print:
- doi:10.1007/s11040-020-09339-1