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

Abstract: In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible non-Newtonian fluids equations equations with initial value conditions. We get new sufficient conditions by means of the Sobolev multiplier spaces, which guarantee the establishment of the energy equality. And the aforementioned equations are often associated with the corresponding positive conclusion of the Onsager's conjecture for non-Newtonian fluids.