Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System
arXiv:1001.1032 · doi:10.1007/s00205-011-0443-x
Abstract
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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Cited by in corpus (14)
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- Suitable weak solutions for the co-rotational Beris-Edwards system in dimension three
- Optimal boundary control of a simplified Ericksen--Leslie system for nematic liquid crystal flows in
- Nonstationary models for liquid crystals: A fresh mathematical perspective
- Global solution to the three-dimensional liquid crystal flows of Q-tensor model
- Entropy inequality and energy dissipation of inertial Qian-Sheng model for nematic liquid crystals
- Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals
- An elementary proof of eigenvalue preservation for the co-rotational Beris-Edwards system
- 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