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arXiv · 1111.1518

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

Mohamad Darwich
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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.

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Mohamad Darwich. 2011-11-07. On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation. https://doi.org/10.1016/j.jde.2012.05.013

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