Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D

Abstract

In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.

32 pages

References in corpus (1)

• Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow

Cited by in corpus (2)

• Uniqueness of weak solutions for the general Ericksen-Leslie system with Ginzburg-Landau penalization in T^2
• Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows