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arXiv · 2103.09259

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

Akansha Sanwal
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Abstract

The Zakharov system in dimension $d\leqslant 3$ 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.

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Akansha Sanwal. 2021-03-16. Local Well-Posedness for the Zakharov System in Dimension $d\leqslant 3$. https://doi.org/10.3934/dcds.2021147

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