Well-Posedness for a Whitham–Boussinesq System with Surface Tension
Journal article, Peer reviewed
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Original versionMathematical Physics, Analysis and Geometry. 2020, 23, 23. 10.1007/s11040-020-09339-1
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.