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The Cauchy problem for Benney-Luke and generalized Benney-Luke equations. (English) Zbl 1212.35315

Summary: We examine the question of the minimal Sobolev regularity required to construct local solutions to the Cauchy problem for the Benney-Luke (BL) and generalized Benney-Luke (gBL) equations. As a consequence we prove that the initial-value problems are globally well-posed in the energy space.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction