Comptes Rendus
no. 1
Partial Differential Equations
Global existence of weak solutions to some micro-macro models
[Existence globale de solutions faibles a quelques modèles micro-macro]

Présenté par : Pierre-Louis Lions

Pierre-Louis Lions1 ; Nader Masmoudi2
1 University Paris-Dauphine, place du Maréchal-De-Lattre-De-Tassigny, 75775 Paris cedex 16, France
2 Courant Institute of Mathematical Sciences, 251, Mercer Street, New York, NY 10012-1185, USA
Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 15-20.

On montre l'existence globale de solutions faibles à certains modèles micro-macro. En particulier on étudie le modèle FENE (le cas des ressorts) et le modèle de Doi (le cas des barres rigides). La preuve est basée sur la propagation de la compacité.

We prove the global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.05.011
Pierre-Louis Lions 1 ; Nader Masmoudi 2

1 University Paris-Dauphine, place du Maréchal-De-Lattre-De-Tassigny, 75775 Paris cedex 16, France
2 Courant Institute of Mathematical Sciences, 251, Mercer Street, New York, NY 10012-1185, USA 
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Pierre-Louis Lions; Nader Masmoudi. Global existence of weak solutions to some micro-macro models. Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 15-20. doi : 10.1016/j.crma.2007.05.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.011/

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