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

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 Schr"odinger initial data $H^{s_k,s^{\mathrm{\prime }}}$ and the wave data $H^{s_l,s^{\mathrm{\prime }}}$ where $s_k > (d-1)/2, s_l > (d-2)/2, s_k - s_l = 1/2$and$s’ > 1/2$.