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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller–Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general,(More)
Molecule spaces have been introduced by Furioli and Terraneo [Funkcial. Ekvac., 45 (2002), pp. 141–160] to study some local behavior of solutions to the Navier–Stokes equations. In this paper we give a new characterization of these spaces and simplify Furioli and Terraneo's result. Our analysis also provides a persistence result for Navier–Stokes in a(More)
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