EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS

Authors

Feng, Y; Li, L; Liu, JG; Xu, X

Abstract

We study the existence of weak solutions to the p-Navier-Stokes equations with a symmetric p-Laplacian on bounded domains. We construct a particular Schauder basis in W01, p(Ω) with divergence free constraint and prove existence of weak solutions using the Galerkin approximation via this basis. Meanwhile, in the proof, we establish a chain rule for the Lp integral of the weak solutions, which fixes a gap in our previous work. The equality of energy dissipation is also established for the weak solutions considered.