Global well-posedness for the dynamical Q-tensor model of liquid crystals

Abstract

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.

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Cited by in corpus (8)

• Global strong solutions of the full Navier-Stokes and $Q$-tensor system for nematic liquid crystal flows in $2D$: existence and long-time behavior
• Suitable weak solutions for the co-rotational Beris-Edwards system in dimension three
• Nonstationary models for liquid crystals: A fresh mathematical perspective
• Global solution to the three-dimensional liquid crystal flows of Q-tensor model
• Global well posedness for a Q-tensor model of nematic liquid crystals
• Global Well-posedness of the Two Dimensional Beris-Edwards System with General Laudau-de Gennes Free Energy
• On the initial boundary value problem of a Navier-Stokes/$Q$-tensor model for liquid crystals
• Rigorous justification of the uniaxial limit from Qian-Sheng's inertial $Q$-tensor theory to the Ericksen-Leslie theory