Preprint C73/2008
The Cauchy problem for the Benney-Luke equation and generalized Benney-Luke equation
Aída Patricia González Nieva
Keywords: Benney-Luke equation
We examine the question of the minimal Sobolev regularity required to construct local solutions to the Cauchy problem for the isotropic Benney-Luke (BL), isotropic {\it p}-generalized Benney-Luke (p-gBL) and generalized Benney-Luke (gBL) equations. The main results in this work regards the global well-posedness of the initial value problem (IVP) associated to the (BL), the (p-gBL) and (gBL) equations in the energy space, $\dot{H}^2(\R^2) \cap \dot{H}^1(\R^2) \times H^1(\R^2)$, the local well-posedness of IVP associated to the (gBL) in $H^s(\R^2)\times H^{s-1}(\R^2)$ for $9/5