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We regard the Cauchy problem for a particular Whitham-Boussinesq systemmodelling surface waves of an inviscid incompressible fluid layer. We areinterested in well-posedness at a very low level of regularity. We derivedispersive and Strichartz estimates, and implement them together with a fixedpoint argument to solve the problem locally. Hamiltonian conservationguarantees global well-posedness for small initial data in the one dimensionalsettings.

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