On the Finite Time Blow-up of Biharmonic Map Flow in Dimension Four

被引：7
作者：
Liu L. [1 ]
Yin H. [2 ]
机构：
[1] University of Science and Technology of China, School of Mathematical Sciences, Hefei
[2] Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Techology of China, Hefei
来源：
Journal of Elliptic and Parabolic Equations | 2015年 / 1卷 / 2期
基金：
中国国家自然科学基金;
关键词：
Biharmonic map flow; finite blow-up; neck analysis;
D O I：
10.1007/BF03377386
中图分类号：
学科分类号：
摘要：
In this paper, we show that for certain initial values, the (extrinsic) biharmonic map flow in dimension four must blow up in finite time. © 2015, Orthogonal Publishing.
引用
收藏
页码：363 / 385
页数：22
相关论文
共 17 条
  • [1] Adams R., Fournier J., Sobolev spaces, (2003)
  • [2] Breiner C., Lamm T., Compactness results for sequences of approximate biharmonic maps, Pacific J. Math., 276, pp. 59-92, (2015)
  • [3] Chang K.-C., Ding W.-Y., Ye R., Finite-time blow-up of the heat flow of harmonic maps from surfaces, J. Differential Geom., 36, 2, pp. 507-515, (1992)
  • [4] Chen J.-Y., Li Y.-X., Homotopy classes of harmonic maps of the stratified 2-spheres and applications to geometric flows, Adv. Math., 263, pp. 357-388, (2014)
  • [5] Cooper M., Critial O(d)-equivariant biharmonic map, Calc. Var. PDE, 54, pp. 2895-2919, (2015)
  • [6] Ding W.-Y., Tian G., Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom., 3, pp. 543-554, (1995)
  • [7] Gastel A., The extrinsic polyharmonic map heat flow in critical dimensions, Adv. Geom., 6, 4, pp. 501-521, (2006)
  • [8] Lamm T., Heat flow for extrinsic biharmonic maps with small initial energy, Ann. Global Anal. Geom., 26, 4, pp. 369-384, (2004)
  • [9] Li Y.-X., Wang Y.-D., A counterexample to the energy identity for sequences of a-harmonic maps, Pacific J. Math., 274, pp. 107-123, (2015)
  • [10] Liu L., Yin H., Neck analysis of biharmonic maps
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