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Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows

Author

Listed:
  • Miho Murata

    (Department of Mathematical and System Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8561, Shizuoka, Japan
    Mathematical Institute, Graduate School of Science, Tohoku University, 6-3 Aramaki, Aza-Aoba, Aoba-ku, Sendai 980-8578, Miyagi, Japan)

Abstract

In this paper, we prove the unique existence of global strong solutions and decay estimates for the simplified Ericksen–Leslie system describing compressible nematic liquid crystal flows in R N , 3 ≤ N ≤ 7 . Firstly, we rewrite the system in Lagrange coordinates, and secondly, we prove the global well-posedness for the transformed system, which is the main task in this paper. The proof is based on the maximal L p - L q regularity and the L p - L q decay estimates to the linearized problem.

Suggested Citation

  • Miho Murata, 2022. "Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows," Mathematics, MDPI, vol. 11(1), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:181-:d:1019139
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