Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows

Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows

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 RN, 3≤N≤7. Firstly, we rewrite the system in Lagrange coordinates, and secondly, we prove the global well-pose...

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Veröffentlicht in:Mathematics (Basel) 2022-12, Vol.11 (1), p.181
1. Verfasser: Murata, Miho
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Compressibility
compressible Navier–Stokes equations
Crystals
Decay
Ericksen–Leslie system
Estimates
Estimation theory
Euclidean space
Food science
global strong solutions
Lagrange coordinates
Liquid crystals
Materials
Mathematical functions
Mechanical properties
Nematic crystals
Twisted nematic liquid crystal displays
Well posed problems
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Beschreibung
Zusammenfassung: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 RN, 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 Lp-Lq regularity and the Lp-Lq decay estimates to the linearized problem.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11010181