Local well-posedness of the Cauchy problem for the degenerate Zakharov system

Abstract

The aim of this paper is to investigate well-posedness of the Cauchy problem for the degenerate Zakharov system. Local well-posedness holds for anisotropic Sobolev data by applying $U^2,V^2$ type spaces. We give the Schrödinger initial data $H^{s_k,s^{\prime }}$ and the wave data $H^{s_l,s^{\prime }}$ where $s_k>(d-1)/2,s_l>(d-2)/2,s_k-s_l=1/2$ and $s^{\prime }>1/2$.

References in corpus (1)

• Convolutions of singular measures and applications to the Zakharov system