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Steady flows of an incompressible homogeneous chemically reacting fluid aredescribed by a coupled system, consisting of the generalized Navier--Stokesequations and convection - diffusion equation with diffusivity dependent on theconcentration and the shear rate. Cauchy stress behaves like power-law fluidwith the exponent depending on the concentration. We prove the existence of aclassical solution for the two dimensional periodic case whenever the power lawexponent is above one and less than infinity.

On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index