Newtonian Limit for Weakly Viscoelastic Fluid Flows

Didier Bresch (1) , Christophe Prange (2)

1 LAMA - Laboratoire de Mathématiques
2 IMB - Institut de Mathématiques de Bordeaux

This article addresses the low Weissenberg asymptotic analysis (Newtonian limit) of some macroscopic models of viscoelastic uid ows in the framework of global weak solutions. We investigate the convergence of the corotational Johnson-Segalman, the FENE-P, the Giesekus and PTT models. Relying on a priori bounds coming from energy or free energy estimates, we rst study the weak convergence toward the Navier-Stokes system. We then turn to the main focus of our paper, i.e. the strong convergence. The novelty of our work is to address these issues by relative entropy estimates, which require the introduction of some corrector terms. We also take into account the presence of defect measures in the initial data, uniform with respect to the Weissenberg number, and prove that they do not perturb the Newtonian limit of the corotational system.

Mots clés: Viscoelasticity; Weisenberg number; Deborah number; relative entropy; free energy; Newtonian limit; weak solutions

Domaines: Equations aux dérivées partielles [math.AP]

Didier Bresch, Christophe Prange. Newtonian Limit for Weakly Viscoelastic Fluid Flows. SIAM Journal on Mathematical Analysis, 2014, 46 (2), pp.1116 - 1159. ⟨10.1137/130923464⟩. ⟨hal-01915577⟩