Energy equality of the weak solutions to non-Newtonian fluids equations

Abstract

In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible non-Newtonian fluid equations with initial value conditions. We derive new sufficient conditions via Sobolev multiplier spaces that guarantee the validity of the energy equality. Moreover, the aforementioned equations are often associated with the uniqueness problem of weak solutions for non-Newtonian fluids, which, in a certain sense, constitutes the positive counterpart of Onsager's conclusion for non-Newtonian fluids.