Energy conservation for the weak solutions of the compressible Navier-Stokes equations

Abstract

In this paper, we prove the energy conservation for the weak solutions of the compressible Navier-Stokes equations for any time $t>0$, under certain conditions. The results hold for the renormalized solutions of the equations with constant viscosities, as well as the weak solutions of the equations with degenerate viscosity. Our conditions do not depend on the dimensions. The energy may conserve on the vacuum for the compressible Navier-Stokes equations with constant viscosities. Our results are the first ones on the energy conservation for the weak solutions of the compressible Navier-Stokes equations.

References in corpus (4)

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• Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
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• Energy Conservation for the Compressible Euler and Navier-Stokes Equations with Vacuum
• A note on weak solutions of conservation laws and energy/entropy conservation
• On the Extension of Onsager's Conjecture for General Conservation Laws
• A new proof to the energy conservation for the Navier-Stokes equations
• The energy equality for the Navier-Stokes equations in bounded domains
• The role of density in the energy conservation for the isentropic compressible Euler equations
• Energy equality in compressible fluids with physical boundaries
• On entropy conservation for general systems of conservation laws
• Energy equality for the isentropic compressible Navier-Stokes equations without upper bound of the density
• A tribute to conservation of energy for weak solutions
• Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions