# Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum

@inproceedings{Ye2021EnergyEI, title={Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum}, author={Yulin Ye and Yaniqng Wang and Wei Wei}, year={2021} }

It is well-known that a Leray-Hopf weak solution in L(0, T ;L(Ω)) for the incompressible Navier-Stokes system is persistence of energy due to Lions [19]. In this paper, it is shown that Lions’s condition for energy balance is also valid for the weak solutions of the isentropic compressible Navier-Stokes equations allowing vacuum under suitable integrability conditions on the density and its derivative. This allows us to establish various sufficient conditions implying energy equality for the…

## One Citation

The role of density in the energy conservation for the isentropic compressible Euler equations

- Mathematics
- 2021

In this paper, we study Onsager’s conjecture on the energy conservation for the isentropic compressible Euler equations via establishing the energy conservation criterion involving the density ̺ ∈…

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