Global well-posedness of the critical Burgers equation in critical Besov spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Miao, Changxing¹  Wu, Gang² 

[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: Burgers equation;    Modulus of continuity;    Fourier localization;    Global well-posedness;    Besov spaces;   

DOI  :  10.1016/j.jde.2009.03.028

来源: Elsevier

【 摘 要 】

We make use of the method of modulus of continuity [A. Kiselev, F. Nazarov, R. Shterenberg, Blow up and regularity for fractal Burgers equation, Dyn. Partial Differ. Equ. 5 (2008) 211-240] and Fourier localization technique [H. Abidi, T. Hmidi, On the global well-posedness of the critical quasi-geostrophic equation, SIAM J. Math. Anal. 40 (1) (2008) 167-185] [H. Abidi, T. Hmidi, On the global well-posedness of the critical quasi-geostrophic equation, SIAM J. Math. Anal. 40 (1) (2008) 167-185] to prove the global well-posedness of the critical Burgers equation partial derivative(t)u+ u partial derivative(x)u + Lambda u = 0 in critical Besov spaces (B) over dot (1/p)(p,1)(R) with p is an element of [1,infinity), where Lambda = root-Delta. (C) 2009 Elsevier Inc. All rights reserved.

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