Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers (Q2788743)

The purpose of this paper is to study the compressible Navier-Stokes-Fokker-Planck equation equation in non-dimensional form, with an elastic extra-stress tensor. The meanings of the constants and the Kramer's expression are described in detail. The main theorem characterizes the existence of a globally weak solution with given initial conditions. The proof uses a formal energy identity, Gronvalls inequality, Schauder's fixed point theorem, Lebesgue interpolation, Gagliardo-Nirenberg inequality, generalized Korn's inequality, Sobolev embedding, Aubin-Lions-Simon compactness theorem, integration by parts, Lax-Milgram theorem, dominated convergence theorem, Poincaré inequality, Egoroff's theorem, Vitali's convergence therem, Dubinski's compactness theorem, Lipschitz continuity, Fatou's lemma, Dunford-Pettis therem, Hölder's inequality, Youngs function, Du Bois-Reymond's lemma, Bogovsky operator, Parseval-Plancherel formula, Riesz operator, Friedrichs mollifier.