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

[摘要] We prove global well-posedness for the Cauchy problem associated with the Kadomtsev-Petviashvili-Burgers equation (KPBII) in R-2 when the initial value belongs to the anisotropic Sobolev space H-s1s2(R-2) for all s(1) > -1/2 and s(2) >= 0. On the other hand, we prove in some sense that our result is sharp. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15