Local well-posedness for the Zakharov system in dimension $d=2,3$

Abstract

The Zakharov system in dimension $d=2,3$ is shown to have a local unique solution for any initial values in the energy space $H^s\times H^l\times H^{l-1}$, where the range of regularity $(s,l)$ is extended, especially at $s=l-1$. The result is obtained mainly by the normal form reduction and the Strichartz estimates.

References in corpus (1)

• Convolutions of singular measures and applications to the Zakharov system