A note on non-uniformly elliptic Stokes-type systems in two variables

Abstract

We consider a Stokes-type system of partial differential equations in 2D, which describes the stationary and also slow flow of an incompressible fluid. Here the nonlinear differential operator related to the stress tensor is generated by a potential H(\varepsilon)=h(\left|\varepsilon\right|) acting on symmetric (2×2)-matrices, where h is a N-function of rather general type leading to a non-uniformly elliptic problem.