Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals

Global Well Posedness for a Q-tensor Model of Nematic Liquid Crystals

In this paper, we prove the global well posedness and the decay estimates for a Q -tensor model of nematic liquid crystals in R N , N ≥ 3 . This system is a coupled system by the Navier–Stokes equations with a parabolic-type equation describing the evolution of the director fields Q . The proof is b...

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Veröffentlicht in:Journal of mathematical fluid mechanics 2022-05, Vol.24 (2), Article 34
Hauptverfasser: Murata, Miho, Shibata, Yoshihiro
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Continuum Physics
Decay
Estimates
Fluid mechanics
Fluid- and Aerodynamics
Liquid crystals
Mathematical analysis
Mathematical Methods in Physics
Nematic crystals
Physics
Physics and Astronomy
Tensors
Theoretical mathematics
Well posed problems
Yoshihiro Shibata
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Zusammenfassung:In this paper, we prove the global well posedness and the decay estimates for a Q -tensor model of nematic liquid crystals in R N , N ≥ 3 . This system is a coupled system by the Navier–Stokes equations with a parabolic-type equation describing the evolution of the director fields Q . The proof is based on the maximal L p – L q regularity and the L p – L q decay estimates to the linearized problem.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-022-00677-4