Well-Posedness for a Dispersive System of the Whitham-Boussinesq Type
Journal article, Peer reviewed
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Original versionSIAM Journal on Mathematical Analysis. 2020, 52 (3), 2353-2382. 10.1137/19M125577X
We regard the Cauchy problem for a particular Whitham--Boussinesq system modeling 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.