BRESCH, Didier; PRANGE, Christophe

doi:10.1137/130923464

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BRESCH, Didier
Laboratoire de Mathématiques [LAMA]

PRANGE, Christophe
Institut de Mathématiques de Bordeaux [IMB]

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SIAM Journal on Mathematical Analysis. 2014-01, vol. 46, n° 2, p. 1116 - 1159

Society for Industrial and Applied Mathematics

Résumé en anglais

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.< Réduire

Mots clés en anglais

Viscoelasticity

Weisenberg number

Deborah number

relative entropy

free energy

Newtonian limit

weak solutions

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Newtonian Limit for Weakly Viscoelastic Fluid Flows

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