Global existence of weak solutions to some micro-macro models

Masmoudi, Nader; Lions, Pierre-Louis

Masmoudi, Nader; Lions, Pierre-Louis (2007), Global existence of weak solutions to some micro-macro models, Comptes Rendus Mathematique, 345, 1, p. 15-20. http://dx.doi.org/10.1016/j.crma.2007.05.011

Type

Article accepté pour publication ou publié

Date

2007

Journal name

Comptes Rendus Mathematique

Volume

345

Number

Publisher

Elsevier

Pages

15-20

Abstract (FR)

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. Pour citer cet article : P.-L. Lions, N. Masmoudi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Abstract (EN)

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. To cite this article: P.-L. Lions, N. Masmoudi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Subjects / Keywords

Doi model; FENE dumbbell model; weak solutions; Equations aux Dérivées Partielles