Regularity results for parabolic systems related to a class of non-Newtonian fluids

被引:148
作者
Acerbi, E
Mingione, G
Seregin, GA
机构
[1] Univ Parma, Dipartimento Matemat, I-43100 Parma, Italy
[2] VA Steklov Math Inst, St Petersburg Branch, St Petersburg 191011, Russia
来源
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2004年 / 21卷 / 01期
关键词
D O I
10.1016/j.anihpc.2002.11.002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a class of parabolic systems of the type: u(t) - div a(x, t, Du) = 0 where the vector field a(x, t, F) exhibits non-standard growth conditions. These systems arise when studying certain classes of non-Newtonian fluids such as electrorheological fluids or fluids with viscosity depending on the temperature. For properly defined weak solutions to such systems, we prove various regularity properties: higher integrability, higher differentiability, partial regularity of the spatial gradient, estimates for the (parabolic) Hausdorff dimension of the singular set. (C) 2003 Elsevier SAS. All rights reserved.
引用
收藏
页码:25 / 60
页数:36
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