On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions

Research output: Contribution to journalArticle

Abstract

We examine the question of uniqueness for the equivariant reduction of the harmonic map heat flow in the energy supercritical dimension d ≥ 3. It is shown that, generically, singular data can give rise to two distinct solutions that are both stable and satisfy the local energy inequality. We also discuss how uniqueness can be retrieved.

Original languageEnglish (US)
Pages (from-to)2247-2299
Number of pages53
JournalCommunications on Pure and Applied Mathematics
Volume70
Issue number12
DOIs
StatePublished - Dec 2017

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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