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Remarks on self-similar solutions for the surface quasi-geostrophic equation and its generalization


Authors: Marco Cannone and Liutang Xue
Journal: Proc. Amer. Math. Soc. 143 (2015), 2613-2622
MSC (2010): Primary 76B03, 35Q31, 35Q35, 35Q86
DOI: https://doi.org/10.1090/S0002-9939-2015-12468-9
Published electronically: February 16, 2015
MathSciNet review: 3326041
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Abstract: We prove some nonexistence results of self-similar singular solutions for the surface quasi-geostrophic equation and its generalization by relying on the fundamental local $ L^p$-inequality of the self-similar quantity.


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Marco Cannone
Affiliation: Université Paris-Est Marne-la-Vallée, Laboratorie d’Analyse et de Mathématiques Appliquées, Cité Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, Cedex 2, France
Email: marco.cannone@univ-mlv.fr

Liutang Xue
Affiliation: Université Paris-Est Marne-la-Vallée, Laboratorie d’Analyse et de Mathématiques Appliquées, Cité Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée, Cedex 2, France
Address at time of publication: School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China
Email: xue_{}lt@163.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12468-9
Keywords: Self-similar solutions, surface quasi-geostrophic equation, non- existence
Received by editor(s): October 11, 2013
Received by editor(s) in revised form: February 5, 2014
Published electronically: February 16, 2015
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

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