RESULTS ON A NAVIER STOKES SYSTEM WITH APPLICATIONS TO ELECTRORHEOLOGICAL FLUID FLOW

Jean Vuillemin

Description

RESULTS ON A NAVIER-STOKES SYSTEM WITH APPLICATIONS TO ELECTRORHEOLOGICAL FLUID FLOW Pierre Dreyfuss1, Norbert Hungerbuhler2 1Mathematics Department, University of Fribourg, Perolles, CH-1700 Fribourg, SWITZERLAND e-mail: 2Mathematics Department, University of Fribourg, Perolles, CH-1700 Fribourg, SWITZERLAND e-mail: Abstract: We study a Navier-Stokes system which is motivated by models for electrorheological fluids. Its principal features are the weak monotonicity as- sumptions we impose on the viscosity tensor. Moreover we allow the viscosity to depend on the velocity in order to cover some of the models in electrorheo- logical theory. We establish existence of a weak solution of the corresponding Navier-Stokes system. AMS Subj. Classification: 35Q30, 76D05 Key Words: Navier-Stokes systems, weak monotonicity conditions, elec- trorheological fluids 1 Introduction 1.1 A Navier-Stokes problem Let ? ? IRn be a bounded open domain with Lipschitz boundary. We consider the following Navier-Stokes system for the velocity u : ? ? [0, T ) ? IRn and 1This work is supported by the Swiss National Science Foundation under the Grant Number 200020-100051/1

• leray-lions operator


• operator methods


• hilbert spaces


• navier-stokes system


• galerkin basis


• s2 ?


• winslow who

Sujets

• Dreyfuss
• Willis
• Number
• Hilbert space

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• Publié par: pefav
• Nombre de lectures: 35
• Poids de l'ouvrage: 1 Mo

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