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Global existence of weak solution for the 2-D Ericksen–Leslie system

  • Meng WangEmail author
  • Wendong Wang
Article

Abstract

We prove the global existence of weak solution for two dimensional Ericksen–Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of the Ericksen–Leslie system in two and three spatial dimensions.

Mathematics Subject Classification

35Q35 35A01 76A15 76D03 

Notes

Acknowledgments

The authors would like to thank Professor Zhifei ZHANG for his suggestion to consider the problem and his some valuable discussions with them. Part of this work is carried out when the first author is visiting Math. Department of Princeton University. Meng is partially supported by NSFC 10931001, 11371316, and Chen-su star project by Zhejiang University. Wendong is supported by “the Fundamental Research Funds for the Central Universities”, NSFC 11301048 and the Institute of Mathematical Sciences of Chinese University of Hong Kong.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang UniversityHangzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.The Institute of Mathematical SciencesThe Chinese University of Hong KongShatin, N.T.Hong Kong

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