Newtonian Limit for Weakly Viscoelastic Fluid Flows
Language
en
Article de revue
This item was published in
SIAM Journal on Mathematical Analysis. 2014-01, vol. 46, n° 2, p. 1116 - 1159
Society for Industrial and Applied Mathematics
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Viscoelasticity
Weisenberg number
Deborah number
relative entropy
free energy
Newtonian limit
weak solutions
Origin
Hal imported