Energy identity for the incompressible Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility

TL;DR

This paper establishes conditions under which weak solutions of the incompressible Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility satisfy an energy identity, advancing theoretical understanding of this coupled fluid system.

Contribution

It provides new sufficient conditions on the velocity field ensuring energy identities for weak solutions, improving prior theoretical results.

Findings

Weak solutions satisfy energy identity under new conditions

Conditions improve understanding of energy behavior in coupled fluid systems

Advances theoretical analysis of Cahn--Hilliard/Navier--Stokes equations

Abstract

We consider the Cahn--Hilliard/Navier--Stokes system with non-degenerate mobility in the space-periodic case, describing the flow of two viscous immiscible and incompressible Newtonian fluids with matched densities. We identify sufficient conditions on the velocity field for weak solutions to satisfy an energy identity, improving previous results on the literature.