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Ann. I. H. Poincar AN 21 (2004) 2560 www.elsevier.com/locate/anihpc

Summary: Ann. I. H. Poincaré ­ AN 21 (2004) 25­60
Regularity results for parabolic systems related to a class
of non-Newtonian fluids
Résultats de régularité pour des systèmes paraboliques liés
à une classe de fluides non Newtoniens
E. Acerbi a,
, G. Mingione a
, G.A. Seregin b
a Dipartimento di Matematica, Università, via M. D'Azeglio 85/a, 43100, Parma, Italy
b Steklov Mathematical Institute, St. Petersburg Branch, 27, Fontanka, 191011, St. Petersburg, Russia
Received 28 October 2002; accepted 26 November 2002
We consider a class of parabolic systems of the type:
ut - diva(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.
2003 Elsevier SAS. All rights reserved.


Source: Acerbi, Emilio - Dipartimento di Matematica, Università degli Studi di Parma
Seregin, Gregory A. - Steklov Institute of Mathematics at St. Petersburg


Collections: Mathematics