Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in \(\mathbb R^2\)

DOI10.1016/j.aim.2012.06.009zbMath1260.35113arXiv1010.4083OpenAlexW2090319190MaRDI QIDQ456759

Min-Chun Hong, Zhouping Xin

Publication date: 16 October 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4083

zbMATH Keywords

Navier-Stokes equationsEricksen-Leslie systemliquid crystals flowOseen-Franck model

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Liquid crystals (76A15) Weak solutions to PDEs (35D30)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• 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
• Existence of infinitely many equilibrium configurations of a liquid crystal system prescribing the same nonconstant boundary value
• Liquid crystal flows in two dimensions
• On the evolution of harmonic mappings of Riemannian surfaces
• Quasilinear parabolic systems under nonlinear boundary conditions
• Existence and partial regularity of static liquid crystal configurations
• The existence of surfaces of constant mean curvature with free boundaries
• Existence and partial regularity results for the heat flow for harmonic maps
• Stable defects of minimizers of constrained variational principles
• Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds
• The Dirichlet energy of mappings with values into the sphere
• On the partial regularity of weak solutions on nonlinear parabolic systems
• Hausdorff measure and the Navier-Stokes equations
• Gradient estimation on Navier-Stokes equations
• Existence of solutions for the Ericksen-Leslie system
• The phase transition between chiral nematic and smectic \(A^*\) liquid crystals
• Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena
• Magnetic Field‐Induced Instabilities in Liquid Crystals
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• ON EQUATIONS OF MOTION FOR LIQUID CRYSTALS
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Nonparabolic dissipative systems modeling the flow of liquid crystals
• Partial regularity of weak solutions of the liquid crystal equilibrium system
• Harmonic Mappings of Riemannian Manifolds

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