On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index

摘要: Abstract We study a system of partial differential equations describing steady flow an incompressible generalized Newtonian fluid, wherein the Cauchy stress is concentration dependent. Namely, we consider coupled Navier–Stokes and convection–diffusion equation with non-linear diffusivity. prove existence weak solution for certain class models by using generalization monotone operator theory which fits into framework Sobolev spaces variable exponent. Such involved since function spaces, where look solution, are “dependent” itself, thus, a priori do not know them. This leads us to principal assumptions on model parameters that ensure Holder continuity present here constructive proof based Galerkin method allows obtain result very general models.