Relative energy inequality and weak-strong uniqueness]{Relative energy inequality and weak-strong uniqueness for an isothermal non-Newtonian compressible fluid

Abstract

Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a~derivation of the relative energy inequality for the weak solutions to these equations. We show that the standard energy inequality implies the relative energy inequality. Consequently, the relative energy inequality allows us to achieve a weak-strong uniqueness result. In other words, we present that the weak solution of the Navier-Stokes system coincides with the strong solution emanated from the same initial conditions as long as the weak solution exists.