Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in $R^2$

Bassam Kojok

Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in $R^2$

Analysis of PDEs 2007-05-23 v2 Mathematical Physics math.MP

Authors: Bassam Kojok

Abstract

We prove global well-posedness for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers equation (KPBII) in $\mathbb R^2$ when the initial value belongs to the anisotropic Sobolev space $H^{s_1,s_2}(\mathbb R^2)$ for all $s_1>-\frac12$ and $s_2\geq0$ . On the other hand, we prove in some sense that our result is sharp.

Keywords

Kadomtsev-Petviashvili-Burgers equation global well-posedness Cauchy problem anisotropic Sobolev space sharp result

Cite

@article{arxiv.math/0605547,
  title  = {Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in $R^2$},
  author = {Bassam Kojok},
  journal= {arXiv preprint arXiv:math/0605547},
  year   = {2007}
}

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31 pages

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