Blow-up analysis for Boltzmann-Poisson equation in Onsager's theory for point vortices with multi-intensities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Suzuki, Takashi¹  Toyota, Yohei² 

[1] Osaka Univ, Ctr Math Modeling & Data Sci, Osaka 5608531, Japan

[2] Osaka Univ, Grad Sch Engn Sci, Dept Syst Innovat, Div Math Sci, Osaka 5608531, Japan

关键词: Blow-up analysis;    YY Li type estimate;    Onsager's theory;    Point vortices;    Boltzmann-Poisson equation;   

DOI  :  10.1016/j.jde.2018.01.036

来源: Elsevier

【 摘 要 】

In this paper we consider the minimizing sequence for some energy functional of an elliptic equation associated with the mean field limit of the point vortex distribution one-sided Borel probability measure. If such a sequence blows up, we derive some estimate which is related to the behavior of solution near the blow-up point. Moreover, we study the two-intensities case to consider the sufficient condition for this estimate. Our main results are new for the standard mean field equation as well. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free