# 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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

14-day Free Trial

Best Deal — 39% off

### Annual Plan

• All the features of the Professional Plan, but for 39% off!
• Billed annually
• No expiration
• For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588$360/year

billed annually

14-day Free Trial