Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in R2

Abstract

We prove global well-posedness for the Cauchy problem associated with the Kadomtsev-Petviashvili-Burgers equation (KPBII) in R2 when the initial value belongs to the anisotropic Sobolev space Hs1, s2 (R2) for all s1 > - frac(1, 2) and s2 ≥ 0. On the other hand, we prove in some sense that our result is sharp. © 2007 Elsevier Inc. All rights reserved.