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In this paper, we will establish the global existence of a suitable weak solution to the Erickson--Leslie system modeling hydrodynamics of nematic liquid crystal flows with kinematic transports for molecules of various shapes in ${mathbb{R}^3}$, which is smooth away from a closed set of (parabolic) Hausdorff dimension at most $frac{15}{7}$.
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the Oseen-Frank model), free interfaces and topological defects which cou
In this paper, we study the active hydrodynamics, described in the Q-tensor liquid crystal framework. We prove the existence of global weak solutions in dimension two and three, with suitable initial datas. By using Littlewood-Paley decomposition, we
For any smooth domain $Omegasubset mathbb{R}^3$, we establish the existence of a global weak solution $(mathbf{u},mathbf{d}, theta)$ to the simplified, non-isothermal Ericksen-Leslie system modeling the hydrodynamic motion of nematic liquid crystals
We create controllable active particles in the form of metal-dielectric Janus colloids which acquire motility through a nematic liquid crystal film by transducing the energy of an imposed perpendicular AC electric field. We achieve complete command o
We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (no