Energy Conservation for the Weak Solutions of the Compressible Navier–Stokes Equations

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 equati...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2017-09, Vol.225 (3), p.1073-1087
Main Author: Yu, Cheng
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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 be conserved on the vacuum for the compressible Navier–Stokes equations with constant viscosities. Our results are the first ones on energy conservation for the weak solutions of the compressible Navier–Stokes equations.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-017-1121-4