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

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40 pages

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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


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