A regularity criterion to the biharmonic map heat flow in 4

We consider the regularity problem under the critical condition to the biharmonic map heat flow from 4 to a smooth compact Riemannian manifold without boundary. Using Gagliardo-Nirenberg inequalities and delicate estimates, the Serrin type regularity criterion for the smooth solutions of biharmonic...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 285; no. 16; p. 1963
Main Authors Fan, Jishan, Gao, Hongjun, Ogawa, Takayoshi, Takahashi, Futoshi
Format Journal Article
LanguageEnglish
French
German
Published Weinheim Wiley Subscription Services, Inc 01.11.2012
Subjects
Brownian motion
Studies
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Summary:We consider the regularity problem under the critical condition to the biharmonic map heat flow from 4 to a smooth compact Riemannian manifold without boundary. Using Gagliardo-Nirenberg inequalities and delicate estimates, the Serrin type regularity criterion for the smooth solutions of biharmonic map heat flow is obtained without assuming a smallness condition on the initial energy. Our result improved the results of Lamm in 5 and 6 and generalized the results of Chang, Wang, Yang 1, Strzelecki 11 and Wang 13, 14 to non-stationary case. [PUBLICATION ABSTRACT]
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201100243