EnglishWe (Dreyfuss P., Hungerbühler, N., 2004, Int. J. of Pure and Appl.Math. 14(2): 241– 271) investigated a class of Navier-Stokes systems which is motivated by models for electrorheological fluids. We obtained an existence result for a weak solution under mild monotonicity assumptions for the viscosity tensor. In this article, we continue the analysis of such systems, but with various notions...Show more…