Global Finite Energy Weak Solutions to the Compressible Nematic Liquid Crystal Flow in Dimension Three
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Publication:5500581
DOI10.1137/15M1007665zbMath1321.35167arXiv1408.4149MaRDI QIDQ5500581
Changyou Wang, Junyu Lin, Baishun Lai
Publication date: 7 August 2015
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1408.4149
PDEs in connection with fluid mechanics (35Q35) Liquid crystals (76A15) Weak solutions to PDEs (35D30) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)
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Cites Work
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- Global weak solutions to the equations of compressible flow of nematic liquid crystals in two dimensions
- Global existence of solutions of the simplified Ericksen-Leslie system in dimension two
- On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals
- Global regularity and uniqueness of weak solution for the 2-D liquid crystal flows
- Strong solutions of the compressible nematic liquid crystal flow
- Compressible hydrodynamic flow of liquid crystals in 1-D
- Hydrostatic theory of liquid crystals
- Liquid crystal flows in two dimensions
- Existence and partial regularity of static liquid crystal configurations
- Harmonic and quasi-harmonic spheres
- Gradient estimates and blow-up analysis for stationary harmonic maps
- Partial regularity of the dynamic system modeling the flow of liquid crystals
- Harmonic and quasi-harmonic spheres. III: Rectifiability of the parabolic defect measure and generalized varifold flows
- The weak solutions to the evolution problems of harmonic maps
- Harmonic and quasi-harmonic spheres. II.
- Globally weak solutions to the flow of compressible liquid crystals system
- Incompressible limit of the compressible nematic liquid crystal flow
- Large-time behaviour of solutions to the Navier-Stokes equations of compressible flow
- Incompressible limit for the compressible flow of liquid crystals
- Blow up criterion for compressible nematic liquid crystal flows in dimension three
- Global weak solution and large-time behavior for the compressible flow of liquid crystals
- Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one
- On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain
- Some constitutive equations for liquid crystals
- Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
- Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three
- Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions
- Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena
- Viscous flow in smectic A liquid crystals
- Nonparabolic dissipative systems modeling the flow of liquid crystals
- On the existence of globally defined weak solutions to the Navier-Stokes equations
