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This paper explores two generalizations of the classical Aubin-Lions Lemma.First we give a sufficient condition to commute weak limit and multiplicationof two functions. We deduce from this criteria a compactness Theorem fordegenerate parabolic equations. Secondly, we state and prove a compactnessTheorem for non-cylindrical domains, including the case of dual estimatesinvolving only divergence-free test functions.

Some variants of the classical Aubin-Lions Lemma