Finite Time Blow-up for Heat Flows of Self-induced Harmonic Maps

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发表日期：

2024年6月15日

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Bo Chen,
You De Wang

摘要

Let Mⁿ be an embedded closed submanifold of ℝ^k+1 or a smooth bounded domain in ℝⁿ, where n ≥ 3. We show that the local smooth solution to the heat flow of self-induced harmonic map will blow up at a finite time, provided that the initial map u₀ is in a suitable nontrivial homotopy class with energy small enough.