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

Zijun Chen; Shengkun Wu

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

Analysis of PDEs 2022-01-07 v2

Authors: Zijun Chen , Shengkun Wu

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.

Keywords

zakharov system local well-posedness energy space normal form reduction strichartz estimates

Cite

@article{arxiv.2103.15347,
  title  = {Local well-posedness for the Zakharov system in dimension $d=2, 3$},
  author = {Zijun Chen and Shengkun Wu},
  journal= {arXiv preprint arXiv:2103.15347},
  year   = {2022}
}

Related papers

View all related →