On the locally self-similar solution of the surface quasi-geostrophic equation with decaying or non-decaying profiles

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• 作者：Liutang Xue ^{xuelt@bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：76B03 ; 35Q31 ; 35Q35 ; 35Q86
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：261
• 期：10
• 页码：5590-5608
• 全文大小：315 K

文摘

Motivated by the numerical simulation and the study on several 1D models, we consider the locally self-similar singular solutions for the surface quasi-geostrophic equation with decaying or non-decaying blowup profiles. Based on a suitable local 25d3967faf64df633ccd72a9a519a" title="Click to view the MathML source">L^p$L^p$-inequality in terms of the profile and the bootstrapping method, we show some exclusion results and derive the asymptotic behavior of the possible blowup profiles.