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

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• 作者：Changxing Miao ; Gang Wu
• 关键词：Burgers equation ; Modulus of continuity ; Fourier localization ; Global well-posedness ; Besov spaces
• 刊名：Journal of Differential Equations
• 出版年：2009
• 出版时间：15 September 2009
• 年：2009
• 卷：247
• 期：6
• 页码：1673-1693
• 全文大小：254 K

文摘

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 ∂_tu+u∂_xu+Λu=0 in critical Besov spaces with p[1,∞), where .