Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The Ericksen–Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress tensor is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally strongly well-posed in the (Formula presented.)-setting, and a dynamical theory is developed. The equilibria are identified and shown to be normally stable. In particular, a local solution extends to a unique, global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the topology of the natural state manifold. In this case, the solution converges exponentially to an equilibrium, in the topology of the state manifold. The above results are proven without any structural assumptions on the Leslie coefficients and in particular without assuming Parodi’s relation.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalMathematische Annalen
DOIs
Publication statusAccepted/In press - 2016 Aug 2
Externally publishedYes

Fingerprint

Topology
Local Solution
Stress Tensor
Nematic Liquid Crystal
Strong Solution
Incompressible Fluid
Bounded Domain
Converge
Coefficient
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

@article{efa5112cee08409a86696f99a3eee9d5,
title = "Dynamics of the Ericksen–Leslie equations with general Leslie stress I: the incompressible isotropic case",
abstract = "The Ericksen–Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress tensor is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally strongly well-posed in the (Formula presented.)-setting, and a dynamical theory is developed. The equilibria are identified and shown to be normally stable. In particular, a local solution extends to a unique, global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the topology of the natural state manifold. In this case, the solution converges exponentially to an equilibrium, in the topology of the state manifold. The above results are proven without any structural assumptions on the Leslie coefficients and in particular without assuming Parodi’s relation.",
author = "Hieber, {Matthias Georg} and Jan Pr{\"u}ss",
year = "2016",
month = "8",
day = "2",
doi = "10.1007/s00208-016-1453-7",
language = "English",
pages = "1--20",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",

}

TY - JOUR

T1 - Dynamics of the Ericksen–Leslie equations with general Leslie stress I

T2 - the incompressible isotropic case

AU - Hieber, Matthias Georg

AU - Prüss, Jan

PY - 2016/8/2

Y1 - 2016/8/2

N2 - The Ericksen–Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress tensor is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally strongly well-posed in the (Formula presented.)-setting, and a dynamical theory is developed. The equilibria are identified and shown to be normally stable. In particular, a local solution extends to a unique, global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the topology of the natural state manifold. In this case, the solution converges exponentially to an equilibrium, in the topology of the state manifold. The above results are proven without any structural assumptions on the Leslie coefficients and in particular without assuming Parodi’s relation.

AB - The Ericksen–Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress tensor is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally strongly well-posed in the (Formula presented.)-setting, and a dynamical theory is developed. The equilibria are identified and shown to be normally stable. In particular, a local solution extends to a unique, global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the topology of the natural state manifold. In this case, the solution converges exponentially to an equilibrium, in the topology of the state manifold. The above results are proven without any structural assumptions on the Leslie coefficients and in particular without assuming Parodi’s relation.

UR - http://www.scopus.com/inward/record.url?scp=84982803732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84982803732&partnerID=8YFLogxK

U2 - 10.1007/s00208-016-1453-7

DO - 10.1007/s00208-016-1453-7

M3 - Article

AN - SCOPUS:84982803732

SP - 1

EP - 20

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -