Existence of weak solutions to $ p $-Navier-Stokes equations

We study the existence of weak solutions to $ p $-Navier-Stokes equations with a symmetric $-Laplacian on bounded domains. construct particular Schauder basis in W_0^{1,p}(\Omega) divergence free constraint and prove using Galerkin approximation via this basis. Meanwhile, proof, we establish chain rule for L^p integral solutions, which fixes gap our previous work. The equality energy dissipation is also established considered.