On a class of electrorheological fluids
type: Item
instance of: scholarly article
title: On a class of electrorheological fluids
zbMATH Open document ID: 1014.76098
author: Valentina Busuioc
author: D. Cioranescu
published in: Ricerche di Matematica
publication date: 2003-04-22T00:00:00Z
review text: The paper deals with flows of a class of electrorheological fluids governed by physical laws which include a nonconstant electrical field. Such a problem is analyzed in view of possible applications in modeling ``smart materials''. The authors deal with Newtonian fluids of dielectric type, whose mathematical study leads to a system of PDE, from which the electrical field can be derived by simply solving Dirichlet problem for a quasilinear elliptic equation. As a consequence, the authors obtain a global existence of weak solution for arbitrary \(L^2\) initial data and under some technical assumptions on the force and electric field. Such solution is shown to be unique in two-dimensional case. In three-dimensional case, for initial velocity in \(H^1\), a regular local (unique) solution is obtained which, in turn, is shown to be global in time under some smallness assumption on the data.
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q60
zbMATH DE Number: 1898304
zbMATH Keywords: small data
zbMATH Keywords: uniqueness
zbMATH Keywords: electrorheological fluids
zbMATH Keywords: nonconstant electrical field
zbMATH Keywords: Newtonian fluids
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: global existence of weak solutions
zbMATH Keywords: regular local unique solution
reviewed by: G. Tarantello
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1898304