Energy equality for the isentropic compressible Navier-Stokes equations without upper bound of the density

TL;DR

This paper establishes energy equality criteria for weak solutions of the isentropic compressible Navier-Stokes equations without requiring an upper bound on the density, broadening the understanding of solution regularity.

Contribution

It introduces new energy equality criteria that do not depend on the density being essentially bounded, extending previous results that required such bounds.

Findings

Energy equality criteria without upper density bounds

Weak solutions with minimal regularity maintain energy equality

Broadens applicability of energy conservation results

Abstract

In this paper, we are concerned with the minimal regularity of both the density and the velocity for the weak solutions keeping energy equality in the isentropic compressible Navier-Stokes equations. The energy equality criteria without upper bound of the density are established. Almost all previous corresponding results requires $\rho\in L^{\infty}(0,T;L^{\infty}(\mathbb{T}^{d}))$.