On the Cauchy problem for a Boussinesq type system

Abstract

We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s({\mathbb{R}}^2){)}^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\times {\mathcal{V}}^{s+1}$ for $s>3/2$ (see below for the definition of ${\mathcal{V}}^s$).

16 pages

References in corpus (2)

• Decay estimates for a class of wave equations
• Well-posednesss of strongly dispersive two-dimensional surface waves Boussinesq systems