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

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

2006-05-19

arxiv.org/abs/math/0605547v2

Mathematics

Analysis of PDEs

31 pages

Scientific paper

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.

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