Abstract
In this article, we prove a regularity criterion for the local strong solutions to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials.
Highlights
1 Introduction In this article, we consider the following simplified version of Ericksen-Leslie system modeling the hydrodynamic flow of compressible, nematic liquid crystals
R is the density, u is the fluid velocity and d represents the macroscopic average of the nematic liquid crystal orientation field, p(r) := arg is the pressure with positive constants a > 0 and g ≥ 1. μ and l are the shear viscosity and the bulk viscosity coefficients of the fluid respectively, which are assumed to satisfy the following physical condition: μ > 0, 3λ + 2μ ≥ 0
For the standard nematic liquid crystal flows, we refer to recent studies in [6,7]
Summary
Introduction In this article, we consider the following simplified version of Ericksen-Leslie system modeling the hydrodynamic flow of compressible, nematic liquid crystals (see: [1,2]) ∂t(ρu) + div(ρu ⊗ u) + ∇p(ρ) − μ u − (λ + μ∇divu = − d · ∇d, (1:2) Ericksen [3] proved the following local-in-time well-posedness: Proposition 1.1. Holds, there exist T0 > 0 and a unique strong solution (r, u, d) to the problem (1.1)-(1.4).
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