Dynamics of the Ericksen–Leslie Equations with General Leslie Stress II

The Compressible Isotropic Case

研究成果: Article

抄録

In this article, the non-isothermal compressible Ericksen–Leslie system for nematic liquid crystals subject to general Leslie stress is considered. It is shown that this system is locally well-posed within the L q -setting and that for initial data close to equilibria points (which are identical with the ones for the incompressible situation), the solution exists globally. Moreover, any global solution which does not develop singularities converges to an equilibrium in the topology of the natural state manifold. Note that no structural assumptions on the Leslie coefficients are imposed and, in particular, Parodi’s relation is not being assumed. The results can be viewed as an extension of the studies in Hieber and Prüss (Math Ann 369:977–996, 2017) for the incompressible case to the compressible situation.

元の言語English
ジャーナルArchive for Rational Mechanics and Analysis
DOI
出版物ステータスPublished - 2019 1 1
外部発表Yes

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Nematic liquid crystals
Topology
Nematic Liquid Crystal
Equilibrium Point
Global Solution
Singularity
Converge
Coefficient

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

これを引用

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abstract = "In this article, the non-isothermal compressible Ericksen–Leslie system for nematic liquid crystals subject to general Leslie stress is considered. It is shown that this system is locally well-posed within the L q -setting and that for initial data close to equilibria points (which are identical with the ones for the incompressible situation), the solution exists globally. Moreover, any global solution which does not develop singularities converges to an equilibrium in the topology of the natural state manifold. Note that no structural assumptions on the Leslie coefficients are imposed and, in particular, Parodi’s relation is not being assumed. The results can be viewed as an extension of the studies in Hieber and Pr{\"u}ss (Math Ann 369:977–996, 2017) for the incompressible case to the compressible situation.",
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T2 - The Compressible Isotropic Case

AU - Hieber, Matthias Georg

AU - Prüss, Jan

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AB - In this article, the non-isothermal compressible Ericksen–Leslie system for nematic liquid crystals subject to general Leslie stress is considered. It is shown that this system is locally well-posed within the L q -setting and that for initial data close to equilibria points (which are identical with the ones for the incompressible situation), the solution exists globally. Moreover, any global solution which does not develop singularities converges to an equilibrium in the topology of the natural state manifold. Note that no structural assumptions on the Leslie coefficients are imposed and, in particular, Parodi’s relation is not being assumed. The results can be viewed as an extension of the studies in Hieber and Prüss (Math Ann 369:977–996, 2017) for the incompressible case to the compressible situation.

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