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Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case q = 3 d d + 2

Jörg Wolf (2007)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider weak solutions 𝐮 : Ω d to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain Ω d ( d = 2 or d = 3 ). For the critical case q = 3 d d + 2 we prove the higher integrability of 𝐮 which forms the basis for applying the method of differences in order to get fractional differentiability of 𝐮 . From this we show the existence of second order weak derivatives of u .

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