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

Abstract

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.

arXiv admin note: text overlap with arXiv:1103.1292

References in corpus (2)

• Global well-posedness of the KP-I initial-value problem in the energy space
• Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in $R^2$

Cited by in corpus (3)

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• Local and global well-posedness for the 2D Zakharov-Kuznetsov-Burgers equation in low regularity Sobolev space
• Analysis of 2+1 diffusive-dispersive PDE arising in river braiding