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On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions
Pierre Germain, Tej‐Eddine Ghoul, Hideyuki Miura
Source abstract
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. © 2017 Wiley Periodicals, Inc.
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