On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions | Zendy

Germain Pierre | Zendy; Ghoul TejEddine | Zendy; Miura Hideyuki | Zendy

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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.

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