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On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions
Author(s) -
Germain Pierre,
Ghoul TejEddine,
Miura Hideyuki
Publication year - 2017
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21716
Subject(s) - uniqueness , harmonic map , mathematics , heat flow , supercritical fluid , equivariant map , flow (mathematics) , dimension (graph theory) , harmonic , mathematical analysis , pure mathematics , geometry , thermodynamics , physics , quantum mechanics , thermal
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. © 2017 Wiley Periodicals, Inc.