Solvability of generalized Navier-Stokes equations

The model Navier-Stokes system of equations depending on the velocity vector, the symmetric part of the gradient, and the pressure is considered in a bounded domain with a Lipschitz boundary. The Navier-Strokes system is a weak perturbation of the strokes system. The methods used in the study are less technical, do not require complicated estimates of the second gradient. The weak solution and the function spaces are defined with the only difference being that X and V are endowed with the Orlicz norm. The study proved an important existence theorem for weak solutions in a certain systems describing electrorheological fluids.