Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System

Details Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System

2010-01-07

arxiv.org/abs/1001.1032v1

Mathematics

Analysis of PDEs

Scientific paper

We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three. We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use the cancellations that allow its existence to prove higher global regularity, in dimension two. We also show the weak-strong uniqueness in dimension two.

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