Differential and Integral Equations

A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions

Francisco Guillén-González and María Ángeles Rodríguez-Bellido

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Abstract

We give a regularity criterion for a $Q$-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary conditions for the tensor $Q$. Starting of a criterion only imposed on the velocity field ${{\textbf{u}}}$ two results are proved; the uniqueness of weak solutions and the global in time weak regularity for the time derivative $(\partial_t {{\textbf{u}}},\partial_t Q)$. This paper extends the work done in [8] for a nematic Liquid Crystal model formulated in $({{\textbf {u}}},{{\textbf {d}}})$, where ${{\textbf {d}}}$ denotes the orientation vector of the liquid crystal molecules.

Article information

Source
Differential Integral Equations, Volume 28, Number 5/6 (2015), 537-552.

Dates
First available in Project Euclid: 30 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1427744100

Mathematical Reviews number (MathSciNet)
MR3328133

Zentralblatt MATH identifier
1340.35261

Subjects
Primary: 35B65: Smoothness and regularity of solutions 35K51: Initial-boundary value problems for second-order parabolic systems 35Q35: PDEs in connection with fluid mechanics 76A15: Liquid crystals [See also 82D30] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

Citation

Guillén-González, Francisco; Rodríguez-Bellido, María Ángeles. A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions. Differential Integral Equations 28 (2015), no. 5/6, 537--552. https://projecteuclid.org/euclid.die/1427744100


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