A regularity criterion to the biharmonic map heat flow in ℜ 4

Jishan Fan, Hongjun Gao, Takayoshi Ogawa, Futoshi Takahashi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We consider the regularity problem under the critical condition to the biharmonic map heat flow from ℜ 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.

Original languageEnglish
Pages (from-to)1963-1968
Number of pages6
JournalMathematische Nachrichten
Issue number16
Publication statusPublished - 2012 Nov


  • 58E20
  • Biharmonic maps
  • Heat flow
  • MSC (2010) 35K55
  • Regularity criteria


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