Comptes Rendus
no. 7
On unique solvability of the full three-dimensional Ericksen–Leslie system
[Sur la solvabilité unique du système tridimensionnel complet d'Ericksen–Leslie]
Gregory A. Chechkin1  ; Tudor S. Ratiu2, 3 ; Maxim S. Romanov1 ; Vyacheslav N. Samokhin4
1 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia
2 Department of Mathematics, Jiao Tong University, 800 Dongchuan Road, Minhang, Shanghai, 200240, China
3 Section de mathématiques, École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland
4 Moscow State University of Printing Arts, 2A, Pryanishnikova ul., Moscow 127550, Russia
Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 459-463.

Dans cet article, nous étudions le système tridimensionnel complet des équations d'Ericksen–Leslie decrivant la nématodynamique des cristaux liquides. Nous donnons la formulation des théorèmes d'existence en temps court et d'unicité des solutions fortes pour le problème de valeur initiale dans le cas périodique et dans un domaine borné avec conditions au bord de types Dirichlet et Neumann.

In this paper, we study the full three-dimensional Ericksen–Leslie system of equations for the nematodynamics of liquid crystals. We announce the short-time existence and uniqueness of strong solutions for the initial value problem in the periodic case and in a bounded domain with Dirichlet- and Neumann-type boundary conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.02.010
Keywords: Liquid crystals, Ericksen–Leslie equations, Nematodynamics, Existence and uniqueness, Director field, Speed of propagation
Mot clés : Cristaux liquides, Équations d'Ericksen–Leslie, Nématodynamique, Existence et unicité, Champ directeur, Vitesse de propagation
Gregory A. Chechkin 1 ; Tudor S. Ratiu 2, 3 ; Maxim S. Romanov 1 ; Vyacheslav N. Samokhin 4

1 Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia
2 Department of Mathematics, Jiao Tong University, 800 Dongchuan Road, Minhang, Shanghai, 200240, China
3 Section de mathématiques, École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland
4 Moscow State University of Printing Arts, 2A, Pryanishnikova ul., Moscow 127550, Russia 
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Gregory A. Chechkin; Tudor S. Ratiu; Maxim S. Romanov; Vyacheslav N. Samokhin. On unique solvability of the full three-dimensional Ericksen–Leslie system. Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 459-463. doi : 10.1016/j.crme.2016.02.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.010/

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[4] G.A. Chechkin; T.S. Ratiu; M.S. Romanov; V.N. Samokhin Nematic liquid crystals. Existence and uniqueness of periodic solutions to Ericksen–Leslie equations, Bull. Ivan Fedorov Mosc. State Univ. Print. Arts, Volume 12 (2012), pp. 139-151

[5] G.A. Chechkin; T.S. Ratiu; M.S. Romanov; V.N. Samokhin Existence and uniqueness theorems for two–dimensional Ericksen–Leslie system, J. Math. Fluid Mech. (2016) | DOI

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☆ GAC was partially supported by RFBR grant 15-01-07920. TSR was partially supported by the NCCR SwissMAP grant of the Swiss National Science Foundation.

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