Regularity results for parabolic systems related to a class of non-Newtonian fluids.
type: Item
instance of: scholarly article
title: Regularity results for parabolic systems related to a class of non-Newtonian fluids.
zbMATH Open document ID: 1052.76004
author: Giuseppe Mingione
author: Emilio Acerbi
author: G. Seregin
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2004-03-15T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78611
review text: The paper studies the regularity of a parabolic system describing electrorheological fluids \( u_t = \text{div } a(x,t,Du)=0\), where the vector field \(a\) exhibits non-standard growth. Such systes may also model other non-Newtonian fluids. A weak solution to the system is found by using additional condition on the growth of solution gradient. Partial \(C^{0,\alpha}\) regularity of spatial gradient of the weak solution is proved. The techniques developed in the paper can be extended to non-homogeneous systems provided the right-hand side satisfies appropriate growth assumptions. Local higher integrability (i.e. the fact that the weak solution and its gradient belong to certain Lebesgue and Sobolev spaces) is proved, and estimates on the parabolic Hausdorff measure of the singular set are given.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 2057151
zbMATH Keywords: weak solution
zbMATH Keywords: electrorheological fluids
zbMATH Keywords: parabolic Hausdorff measure
zbMATH Keywords: non-standard growth
MaRDI profile type: Publication
OpenAlex ID: W2011796284
Wikidata QID: Q58880905
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DOI: 10.1016/J.ANIHPC.2002.11.002
description: scientific article; zbMATH DE number 2057151