Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (4): 1415-1440.doi: 10.1007/s10473-024-0413-7

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WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

Fan YANG, Congming LI*   

  1. School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2023-07-05 Online:2024-08-25 Published:2024-08-30
  • Contact: *E-mail: congming.li@sjtu.edu.cn
  • About author:E-mail: fanyang-m@sjtu.edu.cn
  • Supported by:
    This work was partially supported by NSFC (11831003, 12031012) and the Institute of Modern Analysis-A Frontier Research Center of Shanghai.

Abstract: The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models. In this paper, we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in $\mathbb{R}^3$. Our results yield that if there exists a strong solution, then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Key words: analysis of parabolic and elliptic types, weak-strong uniqueness, active liquid crystals, weak solution, energy equality

CLC Number: 

  • 35A02
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