Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two

Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two In this article we construct a global solution of the simplified Ericksen-Leslie system. We show that the velocity of the solution can be decomposed into the sum of three parts. The main flow is governed by the Oseen vortex with the same circulation Reynolds number as the initial fluid. The secondary flow has finite kinetic energy and decay in the speed (1 + t)−2 as $${t \rightarrow \infty}$$ t → ∞ . The third part is a minor flow whose kinetic energy decays faster than the secondary flow. As for the orientation variable, our solution has a phase function which diverges logarithmically to $${\infty}$$ ∞ as $${t \rightarrow \infty}$$ t → ∞ . This indicates that the orientation variable will keep rotating around the z-axis while $${t \rightarrow \infty}$$ t → ∞ . This phenomenon results from a non-trivial coupling between the orientation variable and a fluid with a non-zero circulation Reynolds number. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

Global m-Equivariant Solutions of Nematic Liquid Crystal Flows in Dimension Two

Loading next page...
 
/lp/springer_journal/global-m-equivariant-solutions-of-nematic-liquid-crystal-flows-in-O0BlneooWG
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1144-x
Publisher site
See Article on Publisher Site

Abstract

In this article we construct a global solution of the simplified Ericksen-Leslie system. We show that the velocity of the solution can be decomposed into the sum of three parts. The main flow is governed by the Oseen vortex with the same circulation Reynolds number as the initial fluid. The secondary flow has finite kinetic energy and decay in the speed (1 + t)−2 as $${t \rightarrow \infty}$$ t → ∞ . The third part is a minor flow whose kinetic energy decays faster than the secondary flow. As for the orientation variable, our solution has a phase function which diverges logarithmically to $${\infty}$$ ∞ as $${t \rightarrow \infty}$$ t → ∞ . This indicates that the orientation variable will keep rotating around the z-axis while $${t \rightarrow \infty}$$ t → ∞ . This phenomenon results from a non-trivial coupling between the orientation variable and a fluid with a non-zero circulation Reynolds number.

Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Jun 24, 2017

References

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
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off