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

By Marius Paicu, Arghir Zarnescu. 2010

134 citations recorded by the source corpus.

We study a complex non-Newtonian fluid that models the flowof 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 cancellations that allow its existence to prove higher global regularity in dimension two. We also show the weak–strong uniqueness in dimension two.

Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5363f83115d8c38fc0111a61229ed15c73c2a6d2

Citations in the corpus

• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, unknown): “We consider the Landau-de Gennes free energy [22] that has been applied to study various phenomena, both analytically (see for example [55, 59]) and numerically (see for example [70, 63, 78]).”