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arXiv · 1902.09438

Well-posedness for a dispersive system of the Whitham-Boussinesq type

Evgueni Dinvay·Sigmund Selberg·Achenef Tesfahun
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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. We are interested in well-posedness at a very low level of regularity. We derive dispersive and Strichartz estimates, and implement them together with a fixed point argument to solve the problem locally. Hamiltonian conservation guarantees global well-posedness for small initial data in the one dimensional settings.

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Evgueni Dinvay, Sigmund Selberg, Achenef Tesfahun. 2019-02-25. Well-posedness for a dispersive system of the Whitham-Boussinesq type. https://arxiv.org/abs/1902.09438

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