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Global existence and asymptotics for an electro-hydrodynamics model

le 23 mai 2012

14H - Groupe de travail "Applications des Mathématiques"

ENS Rennes Bâtiment Sauvy, Salle 5 (rdc)

Séminaire de André Fischer (Technische Universität Darmstadt et ENS Cachan) au groupe de travail "Applications des mathématiques"

Lien vers la page Web de l'orateur Résumé : For an ionic solution in a bounded domain we intend to investigate the evolution of the fluid flow and the concentrations of the solutes. Our model comprises a coupled system of Navier-Stokes and Nernst-Planck equations modeling the velocity field and the concentrations. Concerning the electrical potential a so-called "electro-neutrality condition" is often applied in the literature, which means that the fluid is assumed to be electrically neutral everywhere in the volume. This condition actually reflects reality within the volume, however, in approaching the boundary it is not valid any more, which plays a dominant role e.g. in micro-fluidics. We therefore complement our model by a Poisson equation modeling the electrical potential instead. The resulting system admits a Lyapunov functional which enables us to prove global existence of strong solutions in two dimensions. Using entropy methods it is shown that the solutions converge to a uniquely determined equilibrium state with exponential speed.

Recherche - Valorisation
Erwan Faou et Yannick Privat

Mise à jour le 15 mai 2012