Comptes Rendus
no. 7
Mathematical analysis
Circumventing the lack of dissipation in certain Oldroyd models
[Comment contourner le manque de dissipation de certains modèles de Oldroyd]

Présenté par : Olivier Pironneau

Vivette Girault1 ; L. Ridgway Scott2
1 Sorbonne Universités, UPMC Université Paris-6, CNRS, UMR 7598, Laboratoire Jacques-Louis-Lions, 4, place Jussieu, 75005 Paris, France
2 Departments of Computer Science and Mathematics, Computation Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA
Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 753-759.

Nous modifions le raisonnement utilisé par Renardy pour prouver l'existence et la régularité de solutions d'une sous-classe de modèles de fluides non newtoniens introduits par Oldroyd, comme les modèles maxwelliens de sur-convection et sous-convection. Nous proposons une méthode itérative variationnelle de calcul de solutions qui s'adapte aux éléments finis.

We modify an argument of Renardy proving existence and regularity for a subset of a class of models of non-Newtonian fluids suggested by Oldroyd, including the upper-convected and lower-convected Maxwellian models. We suggest an effective method for solving these models, which can provide a variational formulation suitable for finite element computation.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.05.013
Vivette Girault 1 ; L. Ridgway Scott 2

1 Sorbonne Universités, UPMC Université Paris-6, CNRS, UMR 7598, Laboratoire Jacques-Louis-Lions, 4, place Jussieu, 75005 Paris, France
2 Departments of Computer Science and Mathematics, Computation Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637, USA 
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Vivette Girault; L. Ridgway Scott. Circumventing the lack of dissipation in certain Oldroyd models. Comptes Rendus. Mathématique, Volume 355 (2017) no. 7, pp. 753-759. doi : 10.1016/j.crma.2017.05.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.05.013/

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