González N., A. The Cauchy problem for Benney-Luke and generalized Benney-Luke equations. (English) Zbl 1212.35315 Differ. Integral Equ. 20, No. 12, 1341-1362 (2007). 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. Cited in 3 Documents 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 Keywords:Benney-Luke equation; generalized Benney-Luke equation; Cauchy problem; minimal Sobolev regularity × Cite Format Result Cite Review PDF