On Uniqueness for the Harmonic Map Heat Flow in Supercritical Dimensions |
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| Authors: | Pierre Germain Tej‐Eddine Ghoul Hideyuki Miura |
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| Institution: | 1. Courant Institute, New York University, 251 Mercer St., New York, NY, USA;2. Department of Mathematics, New York University Abu Dhabi, Computational Research Building A2 NYUAD, Saadiyat Island, Abu Dhabi, United Arab Emirates;3. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2‐12‐1, O‐okayama, Meguro, Tokyo 152‐8552, Japan |
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| 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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