Local well-posedness for the Zakharov system in dimension d ≤ 3

The Zakharov system in dimension \begin{document}$ d\leqslant 3 $\end{document} is shown to be locally well-posed in Sobolev spaces \begin{document}$ H^s \times H^l $\end{document}, extending the previously known result. We construct new solution spaces by modifying the \begin{document}$ X^{s,b} $\end{document} spaces, specifically by introducing temporal weights. We use the contraction mapping principle to prove local well-posedness in the same. The result obtained is sharp up to endpoints.