Long-Time existence for a Whitham-Boussinesq system in two dimensions
Tesfahun A.
1 February 2024World Scientific
Communications in Contemporary Mathematics
2024#26Issue 1
This paper is concerned with a two-dimensional Whitham-Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with existence time of scale (μ3/2-2+), where μ and are small parameters related to the level of dispersion and nonlinearity, respectively. In particular, in the KdV regime {μ â }, the existence time is of order-1/2. The main ingredients in the proof are frequency loacalized dispersive estimates and bilinear Strichartz estimates that depend on the parameter μ.
dispersive estimates , long-Time existence , Surface waves , Witham-Boussinesq systems
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Department of Mathematics, Nazarbayev University, Qabanbai Batyr Avenue 53, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics
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