Sufficient conditions for local regularity to the generalized Newtonian fluid with shear thinning viscosity

Abstract

We prove the local regularity of a weak solution \({\varvec{u}}\) to the equations of a generalized Newtonian fluid with power law \(1< q \le 2\) if \({\varvec{u}}\) belongs to a suitable Lebesgue space. This result extends the well-known Serrin condition for weak solutions of the Navier–Stokes equations to the shear-thinning fluids.