Global solution of nematic liquid crystals models
[Solution globale pour modeles de crystaux liquides nématiques]
Guillén-González, Francisco1 ; Rojas-Medar, Marko2
1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Departamento de Matematica Aplicada, IMECC-UNICAMP, C.P. 6065, 13081-970, Campinas-SP, Brazil
Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1085-1090.

Par une méthode de penalisation à partir d'un problème simplifiée de type Ericksen–Leslie, nous démontrons l'existence de solution globale pour le modèle limite de crystaux liquides nématiques. Le point essentiel de la démonstration est une nouvelle propieté de compacité du gradient du vecteur directeur.

We prove existence of a global weak solution for a nematic liquid crystal problem by means of a penalization method using a simplified Ericksen–Leslie model and a new compactness property for the gradient of the director field.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02620-1
Guillén-González, Francisco 1 ; Rojas-Medar, Marko 2

1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
2 Departamento de Matematica Aplicada, IMECC-UNICAMP, C.P. 6065, 13081-970, Campinas-SP, Brazil 
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Guillén-González, Francisco; Rojas-Medar, Marko. Global solution of nematic liquid crystals models. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1085-1090. doi : 10.1016/S1631-073X(02)02620-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02620-1/

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Cité par Sources :

☆ The first author has been partially financed by the projet BFM2000-1317, and the second author by the projects CNPq-Brasil 300116-93-4 and Fapesp-Brasil 01/07557-3.