Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Xu, Xiaojing^1,2  Xue, Liutang³ 

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[3] Univ Paris Est Marne la Vallee, Lab Anal & Math Appl, F-77454 Champs Sur Marne 2, Marne La Vallee, France

关键词: 2D inviscid Boussinesq system;    Yudovich type data;    Critical and supercritical dissipation;    Commutator estimates;   

DOI  :  10.1016/j.jde.2014.01.038

来源: Elsevier

【 摘 要 】

In this paper we consider the Yudovich type solution of the 2D inviscid Boussinesq system with critical and supercritical dissipation. For the critical case, we show that the system admits a global and unique Yudovich type solution; for the supercritical case, we prove the local and unique existence of Yudovich type solution, and the global result under a smallness condition of theta(0). We also give a refined blowup criterion in the supercritical case. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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