Heat Flow of Harmonic Maps Whose Gradients Belong to L^{n}_{x}L^{\infty}_{t} |
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Authors: | Changyou Wang |
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Institution: | (1) Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA |
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Abstract: | For any compact n-dimensional Riemannian manifold (M, g) without boundary, a compact Riemannian manifold without boundary, and 0 < T ≦ +∞, we prove that for n ≧ 4, if u : M × (0, T] → N is a weak solution to the heat flow of harmonic maps such that , then u ∈C
∞(M × (0, T], N). As a consequence, we show that for n ≧3, if 0 < T < +∞ is the maximal time interval for the unique smooth solution u ∈C
∞(M × 0, T), N) of (1.1), then blows up as t ↑ T. |
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Keywords: | |
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