Existence of global weak solutions for unsteady motions of incompressible chemically reacting generalized Newtonian fluids

We study a system of nonlinear partial differential equations describing the unsteady motions incompressible chemically reacting non-Newtonian fluids. The under consideration consists generalized Navier–Stokes with power-law-type stress-strain relation, where power-law index depends on concentration chemical, coupled to convection-diffusion equation for concentration. This arises in rheology synovial fluid found cavities joints. prove existence global weak solutions non-stationary model by using Galerkin method combined monotone operator theory and parabolic De Giorgi–Nash–Moser theory. As governing involve nonlinearity variable index, our proofs exploit framework Sobolev spaces variable-integrability exponent.