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

Mohamad Darwich (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Domaines: Equations aux dérivées partielles [math.AP]

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