Nonuniqueness of nematic liquid crystal flows in dimension three

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of grad...

Regularity of Solutions to 3-d Nematic Liquid Crystal Flows

In this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either u ∈ Lq(0, T ;Lp(R3)), 2 q + 3 p ≤ 1, 3 < p ≤ ∞; or u ∈ Lα(0, T ;Lβ(R3)), 2 α + 3 β ≤ 2, 3 2 < β ≤ ∞, then the solution (u, d) is regular on (0, T ].

Blow up criterion for nematic liquid crystal flows

In this paper, we establish a blow up criterion for the short time classical solution of the nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three. More precisely, 0 < T∗ < +∞ is the maximal time interval iff (i) for n = 3, |ω|+|∇d|2 / ∈ Lt L ∞ x (R × [0, T∗]); and (ii) for n = 2, |...

A Regularity Criterion for the Nematic Liquid Crystal Flows

Nematic Liquid-Crystal Colloids

This article provides a concise review of a new state of colloidal matter called nematic liquid-crystal colloids. These colloids are obtained by dispersing microparticles of different shapes in a nematic liquid crystal that acts as a solvent for the dispersed particles. The microparticles induce a local deformation of the liquid crystal, which then generates topological defects and long-range f...