Non-isothermal General Ericksen–Leslie System: Derivation, Analysis and Thermodynamic Consistency

Francesco De Anna; Chun Liu

doi:10.1007/s00205-018-1287-4

Non-isothermal General Ericksen–Leslie System: Derivation, Analysis and Thermodynamic Consistency

Francesco De Anna, Chun Liu

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We derive a model describing the evolution of a nematic liquid–crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen–Leslie system where the Leslie stress tensor and the Oseen–Frank energy density are considered in their general forms. The work postulate proposed by Ericksen–Leslie is traduced in terms of entropy production.We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.

Original language	English (US)
Pages (from-to)	637-717
Number of pages	81
Journal	Archive for Rational Mechanics and Analysis
Volume	231
Issue number	2
DOIs	https://doi.org/10.1007/s00205-018-1287-4
State	Published - Feb 7 2019

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-018-1287-4

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title = "Non-isothermal General Ericksen–Leslie System: Derivation, Analysis and Thermodynamic Consistency",

abstract = "We derive a model describing the evolution of a nematic liquid–crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen–Leslie system where the Leslie stress tensor and the Oseen–Frank energy density are considered in their general forms. The work postulate proposed by Ericksen–Leslie is traduced in terms of entropy production.We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.",

author = "{De Anna}, Francesco and Chun Liu",

note = "Funding Information: Acknowledgements. The authors express their sincere appreciation to Professor MARIUS PAICU and Professor ARGHIR ZARNESCU for constructive suggestions and discussions. The work Progressed substantially at the Department of Mathematics of the Penn State University. We thank deeply the Department of Mathematics there for their generous support and for providing a stimulating environment in which to work. The work of the second author has been partially supported by the NSF (Grants DMS-1714401 and DMS-1412005). Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Liu, Chun

N1 - Funding Information: Acknowledgements. The authors express their sincere appreciation to Professor MARIUS PAICU and Professor ARGHIR ZARNESCU for constructive suggestions and discussions. The work Progressed substantially at the Department of Mathematics of the Penn State University. We thank deeply the Department of Mathematics there for their generous support and for providing a stimulating environment in which to work. The work of the second author has been partially supported by the NSF (Grants DMS-1714401 and DMS-1412005). Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

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N2 - We derive a model describing the evolution of a nematic liquid–crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen–Leslie system where the Leslie stress tensor and the Oseen–Frank energy density are considered in their general forms. The work postulate proposed by Ericksen–Leslie is traduced in terms of entropy production.We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.

AB - We derive a model describing the evolution of a nematic liquid–crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extension of the general Ericksen–Leslie system where the Leslie stress tensor and the Oseen–Frank energy density are considered in their general forms. The work postulate proposed by Ericksen–Leslie is traduced in terms of entropy production.We finally analyze the global-in-time well-posedness of the system for small initial data in the framework of Besov spaces.

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Non-isothermal General Ericksen–Leslie System: Derivation, Analysis and Thermodynamic Consistency

Abstract

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