Global Well-Posedness for a 1-D Compressible Non-isothermal Model for Nematic Liquid Crystals

2019 ◽  
Vol 168 (1) ◽  
pp. 217-233
Author(s):  
Tong Tang ◽  
Jianzhu Sun
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Well Posedness ◽  
Isothermal Model

scholarly journals On a non-isothermal model for nematic liquid crystals

Nonlinearity ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 243-257 ◽  
Author(s):  
Eduard Feireisl ◽  
Elisabetta Rocca ◽  
Giulio Schimperna
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Isothermal 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.

Sign in / Sign up

Export Citation Format

Share Document