Local Well-Posedness for the Zakharov System in Dimension $d⩽3$

Abstract

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

arXiv comment26 pages, 2 figures

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Cited by in corpus (2)

• The three dimensional stochastic Zakharov system
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