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On a 3D isothermal model for nematic liquid crystals accounting for stretching terms

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Abstract

In the present contribution, we study a PDE system describing the evolution of a nematic liquid crystals flow under kinematic transports for molecules of different shapes. More in particular, the evolution of the velocity field u is ruled by the Navier–Stokes incompressible system with a stress tensor exhibiting a special coupling between the transport and the induced terms. The dynamics of the director field d is described by a variation of a parabolic Ginzburg–Landau equation with a suitable penalization of the physical constraint |d| = 1. Such equation accounts for both the kinematic transport by the flow field and the internal relaxation due to the elastic energy. The main aim of this contribution is to overcome the lack of a maximum principle for the director equation and prove (without any restriction on the data and on the physical constants of the problem) the existence of global in time weak solutions under physically meaningful boundary conditions on d and u.

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Authors and Affiliations

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

    Cecilia Cavaterra & Elisabetta Rocca

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  1. Cecilia Cavaterra
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  2. Elisabetta Rocca
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Correspondence to Elisabetta Rocca.

Additional information

C. Cavaterra was partially supported by MIUR-PRIN Grant 20089PWTPS “Mathematical Analysis for inverse problems towards applications”.

E. Rocca was supported by the FP7-IDEAS-ERC-StG Grant #256872 (EntroPhase).

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Cavaterra, C., Rocca, E. On a 3D isothermal model for nematic liquid crystals accounting for stretching terms. Z. Angew. Math. Phys. 64, 69–82 (2013). https://doi.org/10.1007/s00033-012-0219-7

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  • DOI: https://doi.org/10.1007/s00033-012-0219-7

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