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Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system
journal contribution
posted on 2023-06-07, 23:55 authored by Marius Paicu, Arghir ZarnescuWe 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.
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Publication status
- Published
Journal
Archive for Rational Mechanics and AnalysisISSN
1432-0673Publisher
Springer VerlagExternal DOI
Issue
1Volume
203Page range
45-67Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2013-05-07Usage metrics
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