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Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System

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Abstract

In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.

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Authors and Affiliations

  1. Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, 119991, Russia

    Gregory A. Chechkin & Maxim S. Romanov

  2. Department of Mathematics, Jiao Tong University, 800 Dongchuan Road, Minhang, 200240, Shanghai, China

    Tudor S. Ratiu

  3. Section de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Tudor S. Ratiu

  4. Moscow State University of Printing Art 2A, Pryanishnikova ul., Moscow, 127550, Russia

    Vyacheslav N. Samokhin

Authors
  1. Gregory A. Chechkin
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  2. Tudor S. Ratiu
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  3. Maxim S. Romanov
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  4. Vyacheslav N. Samokhin
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Corresponding author

Correspondence to Tudor S. Ratiu.

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Communicated by M. Hieber

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Chechkin, G.A., Ratiu, T.S., Romanov, M.S. et al. Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System. J. Math. Fluid Mech. 18, 571–589 (2016). https://doi.org/10.1007/s00021-016-0250-0

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  • DOI: https://doi.org/10.1007/s00021-016-0250-0

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