On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation

Details On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation

2011-11-07

arxiv.org/abs/1111.1518v4

Mathematics

Analysis of PDEs

arXiv admin note: text overlap with arXiv:1103.1292

Scientific paper

We prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s >
-1/2$, for the Cauchy problem associated with the
Kadomotsev-Petviashvili-Burgers-I equation (KPBI) by working in Bourgain's type
spaces. This result is almost sharp if one requires the flow-map to be smooth.

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