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arXiv · 1205.2534

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

Sergio Frigeri·Elisabetta Rocca
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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.

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Sergio Frigeri, Elisabetta Rocca. 2012-05-11. Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D. https://doi.org/10.1088/0951-7715%2F26%2F4%2F933

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