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Long-time behavior for a hydrodynamic model on nematic liquid crystal flows with asymptotic stabilizing boundary condition and external force
- Publication Year :
- 2011
-
Abstract
- In this paper, we consider a simplified Ericksen-Leslie model for the nematic liquid crystal flow. The evolution system consists of the Navier-Stokes equations coupled with a convective Ginzburg-Landau type equation for the averaged molecular orientation. We suppose that the Navier-Stokes equations are characterized by a no-slip boundary condition and a time-dependent external force g(t), while the equation for the molecular director is subject to a time-dependent Dirichlet boundary condition h(t). We show that, in 2D, each global weak solution converges to a single stationary state when h(t) and g(t) converge to a time-independent boundary datum h_\infty and 0, respectively. Estimates on the convergence rate are also obtained. In the 3D case, we prove that global weak solutions are eventually strong so that results similar to the 2D case can be proven. We also show the existence of global strong solutions, provided that either the viscosity is large enough or the initial datum is close to a given equilibrium.<br />38 pages
- Subjects :
- Applied Mathematics
Weak solution
Mathematical analysis
Mathematics::Analysis of PDEs
Boundary (topology)
Orientation (vector space)
Physics::Fluid Dynamics
Computational Mathematics
symbols.namesake
Mathematics - Analysis of PDEs
Flow (mathematics)
Liquid crystal
Dirichlet boundary condition
FOS: Mathematics
symbols
Boundary value problem
35B40, 35Q35, 76A15, 76D05
Analysis
Stationary state
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....b90c9b0ac3089c47ed96dec2545d745a