Vol. 276, No. 2, 2015

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ISSN: 0030-8730
A mean field type flow, II: Existence and convergence

Jean-Baptiste Castéras

Vol. 276 (2015), No. 2, 321–345
Abstract

This paper is the continuation of (Castéras 2015), in which we investigated a gradient flow related to the mean field type equation. First, we show that this flow exists for all time. Next, using the compactness result of Castéras (2015), we prove, under a suitable hypothesis on its energy, the convergence of the flow to a solution of the mean field type equation. We also get a divergence result if the energy of the initial data is largely negative.

Keywords
mean field equation, blow-up analysis, geometric flow
Mathematical Subject Classification 2010
Primary: 35B33, 35J20, 53C44, 58E20
Milestones
Received: 14 June 2014
Revised: 2 December 2014
Accepted: 9 January 2015
Published: 15 July 2015
Authors
Jean-Baptiste Castéras
UFRGS, Instituto de Matemática
Av. Bento Goncalves 9500
91540-000 Porto Alegre-RS
Brazil