Well-posedness of the full Ericksen–Leslie model of nematic liquid crystals

2001 ◽  
Vol 333 (10) ◽  
pp. 919-924 ◽  
Author(s):  
Daniel Coutand ◽  
Steve Shkoller
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Well Posedness ◽  
Leslie Model

scholarly journals Entropy inequality and energy dissipation of inertial Qian–Sheng model for nematic liquid crystals

2021 ◽  
Vol 18 (01) ◽  
pp. 221-256
Author(s):  
Ning Jiang ◽  
Yi-Long Luo ◽  
Yangjun Ma ◽  
Shaojun Tang
Keyword(s):  
Liquid Crystals ◽  
Energy Dissipation ◽  
Nematic Liquid Crystals ◽  
Entropy Inequality ◽  
Small Data ◽  
Well Posedness ◽  
Smooth Solutions ◽  
Large Initial Data ◽  
Decay Of Solutions ◽  
Local Solutions

For the inertial Qian–Sheng model of nematic liquid crystals in the [Formula: see text]-tensor framework, we illustrate the roles played by the entropy inequality and energy dissipation in the well-posedness of smooth solutions when we employ energy method. We first derive the coefficients requirements from the entropy inequality, and point out the entropy inequality is insufficient to guarantee energy dissipation. We then introduce a novel Condition (H) which ensures the energy dissipation. We prove that when both the entropy inequality and Condition (H) are obeyed, the local in time smooth solutions exist for large initial data. Otherwise, we can only obtain small data local solutions. Furthermore, to extend the solutions globally in time and obtain the decay of solutions, we require at least one of the two conditions: entropy inequality, or [Formula: see text], which significantly enlarge the range of the coefficients in previous works.

scholarly journals Concentration-cancellation in the Ericksen–Leslie model

2020 ◽  
Vol 59 (6) ◽  
Author(s):  
Joshua Kortum
Keyword(s):  
Steady State ◽  
Liquid Crystals ◽  
Euler Equations ◽  
Weak Solutions ◽  
Nematic Liquid Crystals ◽  
Stability Of Solutions ◽  
Weak Stability ◽  
Ginzburg Landau ◽  
Leslie Model

AbstractWe establish the subconvergence of weak solutions to the Ginzburg–Landau approximation to global-in-time weak solutions of the Ericksen–Leslie model for nematic liquid crystals on the torus $${\mathbb {T}^2}$$ T 2 . The key argument is a variation of concentration-cancellation methods originally introduced by DiPerna and Majda to investigate the weak stability of solutions to the (steady-state) Euler equations.

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