Global well-posedness for a modified critical dissipative quasi-geostrophic equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Miao, Changxing¹  Xue, Liutang² 

[1] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

[2] China Acad Engn Phys, Grad Sch, Beijing 100088, Peoples R China

关键词: Modified quasi-geostrophic equation;    Modulus of continuity;    Blowup criterion;    Global well-posedness;   

DOI  :  10.1016/j.jde.2011.08.018

来源: Elsevier

【 摘 要 】

In this paper we consider the following modified quasi-geostrophic equation partial derivative(t)theta + u . del theta + v|D|(alpha)theta = 0, u = |D|R-alpha-1(perpendicular to)theta, x is an element of R-2 with v > 0 and alpha is an element of ]0, 1[U]1, 2[. When alpha is an element of ]0, 1[, the equation was firstly introduced by Constantin, Iyer and Wu (2008) in [11]. Here, by using the modulus of continuity method, we prove the global well-posedness of the system. As a byproduct, we also show that for every alpha is an element of ]0, 2[, the Lipschitz norm of the solution has a uniform exponential upper bound. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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