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

Abstract : We prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s > -\frac{1}{2}$, 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.

https://hal.archives-ouvertes.fr/hal-00638412
Submitted on : Wednesday, December 21, 2011 - 10:50:10 AM
Last modification on : Thursday, March 5, 2020 - 5:33:30 PM
Document(s) archivé(s) le : Thursday, March 22, 2012 - 2:25:17 AM

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### Citation

Mohamad Darwich. On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation.. Journal of Differential Equations, Elsevier, 2012, Volume 253 (5), pp.1584-1603. ⟨10.1016/j.jde.2012.05.013⟩. ⟨hal-00638412v4⟩

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