WELL-POSEDNESS AND GLOBAL ATTRACTORS FOR LIQUID CRYSTALS ON RIEMANNIAN MANIFOLDS

DOI10.1081/PDE-120004895zbMath1011.35029arXivmath/0101203MaRDI QIDQ3149954

Steve Shkoller

Publication date: 26 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0101203

zbMATH Keywords

contraction mapping argumentLagrangian averaged liquid crystal equationsNavier-Stokes Ginzburg-Landau model

Mathematics Subject Classification ID

Related Items (27)

Global strong solution for the incompressible flow of liquid crystals with vacuum in dimension two ⋮ Blow-up criterion for incompressible nematic type liquid crystal equations in three-dimensional space ⋮ Mixed formulation, approximation and decoupling algorithm for a penalized nematic liquid crystals model ⋮ Existence and uniqueness theorems for the two-dimensional Ericksen-Leslie system ⋮ Trajectory attractors for binary fluid mixtures in 3D ⋮ Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows ⋮ Recent developments of analysis for hydrodynamic flow of nematic liquid crystals ⋮ On a 3D isothermal model for nematic liquid crystals accounting for stretching terms ⋮ Homogenization of the equations of dynamics of nematic liquid crystals with inhomogeneous density ⋮ Existence and uniqueness theorems for the full three-dimensional Ericksen–Leslie system ⋮ Finite-dimensional global attractor for a system modeling the \(2D\) nematic liquid crystal flow ⋮ Global strong solutions to the one-dimensional full compressible liquid crystal equations with temperature-dependent heat conductivity ⋮ Martingale solutions of nematic liquid crystals driven by pure jump noise in the Marcus canonical form ⋮ On a regularized family of models for homogeneous incompressible two-phase flows ⋮ Existence and uniqueness theorems in two-dimensional nematodynamics. Finite speed of propagation ⋮ Pullback attractors of the two-dimensional non-autonomous simplified Ericksen-Leslie system for nematic liquid crystal flows ⋮ Asymptotic behavior of two-dimensional stochastic nematic liquid crystal flows with multiplicative noise ⋮ Nonexistence of smooth solutions for a full viscous isentropic liquid crystal system in three dimensions ⋮ A new approach to non-isothermal models for nematic liquid crystals ⋮ Existence and regularity for a model of viscous oriented fluid accounting for second-neighbor spin-to-spin interactions ⋮ Well-posedness for the three-dimensional compressible liquid crystal flows ⋮ Some results on the penalised nematic liquid crystals driven by multiplicative noise: weak solution and maximum principle ⋮ Global solution of nematic liquid crystals models ⋮ Nematodynamics and random homogenization ⋮ Random attractor for the 2D stochastic nematic liquid crystals flows ⋮ A 3D isothermal model for nematic liquid crystals with delay terms ⋮ Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise

Cites Work

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• Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
• The Camassa-Holm equations and turbulence
• Existence and partial regularity results for the heat flow for harmonic maps
• Existence of solutions for the Ericksen-Leslie system
• Global analysis in mathematical physics. Geometric and stochastic methods. Transl. from the Russian by V. L. Ginzburg.
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Well-posedness of the full Ericksen–Leslie model of nematic liquid crystals
• Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena
• A connection between the Camassa–Holm equations and turbulent flows in channels and pipes
• Nonparabolic dissipative systems modeling the flow of liquid crystals
• Approximation of Liquid Crystal Flows
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory

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