Global existence of weak solutions to some micro-macro models

Pierre-Louis Lions; Nader Masmoudi

doi:10.1016/j.crma.2007.05.011

Partial Differential Equations

Global existence of weak solutions to some micro-macro models

Presented by: Pierre-Louis Lions

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

Comptes Rendus. Mathématique, Volume 345 (2007) no. 1, pp. 15-20.

Abstract
Résumé

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.

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.

Received: 2007-03-29
Accepted: 2007-05-15
Published online: 2007-07-01

DOI: 10.1016/j.crma.2007.05.011

Author's affiliations:

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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     title = {Global existence of weak solutions to some micro-macro models},
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     language = {en},
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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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