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).
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