Well-posednesss of strongly dispersive two-dimensional surface waves Boussinesq systems

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We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the "KdV-KdV" system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical KdV equation.