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A New Approach to Non-Isothermal Models for Nematic Liquid Crystals

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Abstract

We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical thermodynamics. The resulting system of equations captures all essential features of physically relevant models; in particular, the effect of stretching of the director field is taken into account. In addition, the associated initial-boundary value problem admits global-in-time weak solutions without any essential restrictions on the size of the initial data.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via del Politecnico, 1, 00133, Rome, Italy

    Michel Frémond

  3. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133, Milan, Italy

    Elisabetta Rocca

  4. Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Giulio Schimperna

Authors
  1. Eduard Feireisl
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  2. Michel Frémond
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  3. Elisabetta Rocca
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  4. Giulio Schimperna
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Corresponding author

Correspondence to Giulio Schimperna.

Additional information

Communicated by F. Lin

The work of Eduard Feireisl was partially supported by Grant 201/09/0917 of GA ČR in the framework of research programmes supported by AVČR Institutional Research Plan AV0Z10190503 and by the FP7-IDEAS-ERC-StG Grant #256872 (EntroPhase).

The work of Elisabetta Rocca was supported by the FP7-IDEAS-ERC-StG Grant #256872 (EntroPhase).

The work of Giulio Schimperna was supported by the MIUR-PRIN Grant 2008ZKHAHN “Phase transitions, hysteresis and multiscaling”.

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Feireisl, E., Frémond, M., Rocca, E. et al. A New Approach to Non-Isothermal Models for Nematic Liquid Crystals. Arch Rational Mech Anal 205, 651–672 (2012). https://doi.org/10.1007/s00205-012-0517-4

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  • DOI: https://doi.org/10.1007/s00205-012-0517-4

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