LOCAL WELL-POSEDNESS FOR THE ZAKHAROV SYSTEM IN DIMENSION d <= 3

Sanwal A. LOCAL WELL-POSEDNESS FOR THE ZAKHAROV SYSTEM IN DIMENSION d &lt;= 3. Discrete and Continuous Dynamical Systems. Series A. 2022;42(3):1067-1103.The Zakharov system in dimension d <= 3 is shown to be locally well-posed in Sobolev spaces H-s x H-l, extending the previously known result. We construct new solution spaces by modifying the X-s,X-b 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