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.
Regularity results for parabolic systems related to a class of Non Newtonian fluids / Acerbi, Emilio Daniele Giovanni; Mingione, Giuseppe; Seregin, G. A.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 21:(2004), pp. 25-60. [10.1016/j.anihpc.2002.11.002]
Regularity results for parabolic systems related to a class of Non Newtonian fluids
ACERBI, Emilio Daniele Giovanni;MINGIONE, Giuseppe;
2004-01-01
Abstract
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.| File | Dimensione | Formato | |
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