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hal-00638412, version 4

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

Résumé : 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.