Global well-posedness of the non-isothermal model for incompressible nematic liquid crystals

Global well-posedness of the non-isothermal model for incompressible nematic liquid crystals In this paper, a macromolecular non-isothermal model for the incompressible hydrodynamics flow of nematic liquid crystals on T 3 $\mathbb {T}^{3}$ is considered. By a Galerkin approximation, we prove the local existence of a unique strong solution if the initial data u 0 $u_{0}$ , d 0 $d_{0}$ and θ 0 $\theta_{0}$ satisfy some natural conditions and provided that the viscosity coefficients μ and the heat conductivity κ, h, which are temperature dependent, are properly differentiable and bounded. Moreover, with small initial data, we can extend the local strong solution to be a global one by the argument of contradiction. In this case, the exponential time decay rate is also established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Boundary Value Problems Springer Journals

Global well-posedness of the non-isothermal model for incompressible nematic liquid crystals

, Volume 2017 (1) – Aug 9, 2017
23 pages

/lp/springer_journal/global-well-posedness-of-the-non-isothermal-model-for-incompressible-h7KvG3aVZT
Publisher
Springer International Publishing
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general
eISSN
1687-2770
D.O.I.
10.1186/s13661-017-0844-3
Publisher site
See Article on Publisher Site

Abstract

In this paper, a macromolecular non-isothermal model for the incompressible hydrodynamics flow of nematic liquid crystals on T 3 $\mathbb {T}^{3}$ is considered. By a Galerkin approximation, we prove the local existence of a unique strong solution if the initial data u 0 $u_{0}$ , d 0 $d_{0}$ and θ 0 $\theta_{0}$ satisfy some natural conditions and provided that the viscosity coefficients μ and the heat conductivity κ, h, which are temperature dependent, are properly differentiable and bounded. Moreover, with small initial data, we can extend the local strong solution to be a global one by the argument of contradiction. In this case, the exponential time decay rate is also established.

Journal

Boundary Value ProblemsSpringer Journals

Published: Aug 9, 2017

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