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Blow-up and global existence for heat flows of harmonic maps

Yunmei Chen

ICTP, PO Box 586, I-34100 Triest, Italy

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and

Wei-Yue Ding

Institute of Mathematics, Academia Sinica, Beijing, China

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https://doi.org/10.1142/9789813220881_0016Cited by:1 (Source: Crossref)

Abstract:

In this paper it is proved that the solution to the evolution problem for harmonic maps blows up in finite time, if the initial map belongs to some nontrivial homotopy class and the initial energy is sufficiently small.