On the Existence of Classical Solution to the Steady Flows of Generalized Newtonian Fluid with Concentration Dependent Power-Law Index

Abstract

Steady flows of an incompressible homogeneous chemically reacting fluid are described by a coupled system, consisting of the generalized Navier-Stokes equations and convection-diffusion equation with diffusivity dependent on the concentration and the shear rate. Cauchy stress behaves like power-law fluid with the exponent depending on the concentration.

We prove the existence of a classical solution for the two dimensional periodic case whenever the power law exponent is above one and less than infinity.

Keywords

• Synovial fluid
• C-1,C-alpha regularity
• Generalized viscosity
• Variable exponent
• Steady p-Navier-Stokes system