Well-posedness results for the 3D Zakharov-Kuznetsov equation

Francis Ribaud; Stéphane Vento

Well-posedness results for the 3D Zakharov-Kuznetsov equation

Analysis of PDEs 2011-11-14 v1

Authors: Francis Ribaud , Stéphane Vento

Abstract

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\R^3)$ , $s>1$ , as well as in the Besov space $B^{1,1}_2(\R^3)$ . The proof is based on a sharp maximal function estimate in time-weighted spaces.

Keywords

well-posedness

Cite

@article{arxiv.1111.2850,
  title  = {Well-posedness results for the 3D Zakharov-Kuznetsov equation},
  author = {Francis Ribaud and Stéphane Vento},
  journal= {arXiv preprint arXiv:1111.2850},
  year   = {2011}
}

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