Local well-posedness of the Cauchy problem for the degenerate Zakharov system

Isao Kato

Local well-posedness of the Cauchy problem for the degenerate Zakharov system

Analysis of PDEs 2021-03-10 v1

Authors: Isao Kato

Abstract

The aim of this paper is to investigate well-posedness of the Cauchy problem for the degenerate Zakharov system. Local well-posedness holds for anisotropic Sobolev data by applying $U^2, V^2$ type spaces. We give the Schr\"odinger initial data $H^{s_k, s'}$ and the wave data $H^{s_l, s'}$ where $s_k > (d-1)/2, s_l > (d-2)/2, s_k - s_l = 1/2$ and $s' > 1/2$ .

Keywords

degenerate zakharov system cauchy problem local well-posedness anisotropic sobolev spaces u2 and v2 spaces

Cite

@article{arxiv.2103.05340,
  title  = {Local well-posedness of the Cauchy problem for the degenerate Zakharov system},
  author = {Isao Kato},
  journal= {arXiv preprint arXiv:2103.05340},
  year   = {2021}
}

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