A regularity criterion to the biharmonic map heat flow in ℜ4 |
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| Authors: | Jishan Fan Hongjun Gao Takayoshi Ogawa Futoshi Takahashi |
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| Affiliation: | 1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, P. R. China;2. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210046, P. R. China;3. Mathematical Institute, Tohoku University, Sendai, 980‐8578, Japan;4. Department of Mathematics, Osaka City University, 3‐3‐138 Sugimoto, Sumiyoshi‐Ku, Osaka 558‐8585, Japan |
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| Abstract: | 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. |
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| Keywords: | Biharmonic maps heat flow regularity criteria MSC (2010) 35K55 58E20 |
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