Mv-strong uniqueness for density dependent, non-Newtonian, incompressible fluids

Abstract

We consider density dependent, non-Newtonian, incompressible system with the space being flat torus. The viscious stress in the momentum equation is understood through the rheological law and its connection to the proper convex potential. We define the dissipative measure-valued solutions for the aforementioned equations as well as provide a proof of its existence. The main result of this work is the mv-strong uniqueness of the defined solutions.

Analysis of the generalised Aw-Rascle model

“…Remark 3 In a more recent development, Abbatiello, Feireisl and Novotný [1] and Woźnicki [44] simplified the notion of measure-valued solutions to the so-called dissipative solutions (with no Young measure), for both compressible and incompressible Navier-Stokes systems with a general viscosity law describing non-Newtonian fluids. The same can also be used for compressible Euler systems, see Breit,Feireisl,and Hofmanová [4].…”