On regularizing-rate estimates for solutions to the heat flow with initial value problem |
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| Authors: | Meng Wang XiaoFeng Liu |
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| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
2. Department of Applied Mathematics, School of Sciences, Donghua University, Shanghai, 210000, China
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| Abstract: | For a compact Riemannian manifold N ? ? K without boundary, we establish the existence of strong solutions to the heat flow for harmonic maps from ? n to N, and the regularizing rate estimate of the strong solutions. Moreover, we obtain the analyticity in spatial variables of the solutions. The uniqueness of the mild solutions in C([0, T];W 1,n ) is also considered in this paper. |
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