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

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Abstract

We prove global well-posedness for the Cauchy problem associated with the Kadomtsev-Petviashvili-Burgers equation (KPBII) in R2when 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.

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Kojok, B. (2007). Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in R2. Journal of Differential Equations, 242(2), 211–247. https://doi.org/10.1016/j.jde.2007.08.010

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