Global existence of weak solutions to some micro-macro models

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Global existence of weak solutions to macroscopic models of polymeric flows (2011, background): “Global existence of weak solutions was proved in [38] for the co-rotational model.”
Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress (2012, background): “ of the polymers was proved in a sequence of papers, the most recent of which is ([1]). Global existence of weak solutions via propagation of compactness was proved under the corotational assumption ([24], [25]) and, very recently, for the full FENE model ([28]). There is no such result for the Oldr”
Global well posedness for the Maxwell-Navier-Stokes system in 2D (2010, background): “Moreover, ideas based on the propagation of compactness used in [24] and [25] seem not to work here.”
Remarks on the blowup criteria for Oldroyd models (2009, background): “3), the authors in [5] use a losing a priori estimate for solutions of transport equations which was developed by Bahouri and Chemin [1] and used later on by a lot of authors (for example, see [6, 5, 7, 16, 21, 18, 19] and the references therein).”