Blow-up analysis for Neri's mean field equation in 2D-turbulence. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Toyota, Yohei
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 2316
• Page End: 2341
• Publication Date: 2022-04-13
• Subjects: R. Magnanini; Blow-up analysis -- Nonlinear elliptic equation -- Mean field equation -- Point vortices; 35J61 -- 39B52 -- 76F99; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1807009
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper we study the blow-up analysis for some mean field equation on point vortices which is derived by C. Neri under a stochastic assumption. In particular, we derive some estimate which is the asymptotic behavior of blow-up solutions near the blow-up points. To obtain this result we shall employ the new scaling argument for blow-up solutions of Neri's mean field equation. Moreover, we also study the power type elliptic equation in higher dimension case related to mean field equation and derive such estimate.