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Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential

Analysis of PDEs 2012-11-27 v1 Mathematical Physics math.MP

Abstract

We study the existence, regularity and so-called `strict physicality' of weak solutions of a coupled Navier-Stokes Q-tensor system which is proposed as a model for the incompressible flow of nematic liquid crystal materials. An important contribution to the dynamics comes from a singular potential introduced by John Ball and Apala Majumdar (Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst., Vol. 525: pp. 1-11, 2010) which replaces the commonly employed Landau-de Gennes bulk potential. This is built into our model to ensure that a natural physical constraint on the eigenvalues of the Q-tensor order parameter is respected by the dynamics of the system.

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Cite

@article{arxiv.1211.6083,
  title  = {Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential},
  author = {Mark Wilkinson},
  journal= {arXiv preprint arXiv:1211.6083},
  year   = {2012}
}

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26 pages