Advances in Differential Equations

Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions

Helmut Abels, Georg Dolzmann, and YuNing Liu

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Abstract

Existence and uniqueness of local strong solutions for the Beris--Edwards model for nematic liquid crystals, which couples the Navier-Stokes equations with an evolution equation for the $Q$-tensor, is established on a bounded domain $\Omega\subset\mathbb{R}^d$ in the case of homogeneous Dirichlet boundary conditions. The classical Beris--Edwards model is enriched by including a dependence of the fluid viscosity on the $Q$-tensor. The proof is based on a linearization of the system and Banach's fixed-point theorem.

Article information

Source
Adv. Differential Equations Volume 21, Number 1/2 (2016), 109-152.

Dates
First available in Project Euclid: 23 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1448323166

Mathematical Reviews number (MathSciNet)
MR3449332

Zentralblatt MATH identifier
1333.35174

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Abels, Helmut; Dolzmann, Georg; Liu, YuNing. Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions. Adv. Differential Equations 21 (2016), no. 1/2, 109--152. https://projecteuclid.org/euclid.ade/1448323166.


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