JournalsaihpcVol. 28, No. 5pp. 743–773

Selfsimilar expanders of the harmonic map flow

  • Pierre Germain

    Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, USA

  • Melanie Rupflin

    Warwick Mathematics Institute, University of Warwick, Coventry, United Kingdom
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Abstract

We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissible initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so-called equator maps.

Résumé

On étudie lʼexistence, lʼunicité et la stabilité de solutions auto-similaires issues dʼune singularité, pour le flot gradient des applications harmoniques, dans le cadre équivariant. On montre lʼexistence de telles solutions auto-similaires, et comment leurs propriétés dʼunicité et de stabilité sont étroitement reliées à la minimisation ou non de lʼénergie de Dirichlet par lʼapplication équateur.

Cite this article

Pierre Germain, Melanie Rupflin, Selfsimilar expanders of the harmonic map flow. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 5, pp. 743–773

DOI 10.1016/J.ANIHPC.2011.06.004