• Corpus ID: 237267068

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… 
1 Citations
The role of density in the energy conservation for the isentropic compressible Euler equations
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 ̺ ∈

References

SHOWING 1-10 OF 33 REFERENCES
Energy conservation via a combination of velocity and its gradient in the Navier-Stokes system
In the spirit of recent work [15], it is shown that v ∈ L 2p p−1 (0, T ;L 2q q−1 (T)) and ∇v ∈ L(0, T ;L(T)) imply the energy equality in homogeneous incompressible NavierStokes equations and
Refined blow-up criteria for the full compressible Navier–Stokes equations involving temperature
In this paper, inspired by the study of the energy flux in local energy inequality of the 3D incompressible Navier-Stokes equations, we improve almost all the blow up criteria involving temperature
Energy conservation for the compressible Euler and Navier–Stokes equations with vacuum
We consider the compressible isentropic Euler equations on $\mathbb{T}^d\times [0,T]$ with a pressure law $p\in C^{1,\gamma-1}$, where $1\le \gamma <2$. This includes all physically relevant cases,
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
Energy Equality in Compressible Fluids with Physical Boundaries
TLDR
The main idea is to construct a global mollification combined with an independent boundary cut-off, and then take a double limit to prove the convergence of the resolved energy.
On the energy equality for the 3D Navier–Stokes equations
In this paper we study the problem of energy conservation for the solutions of the initial boundary value problem associated to the 3D Navier-Stokes equations, with Dirichlet boundary conditions.
The Energy Balance Relation for Weak solutions of the Density-Dependent Navier-Stokes Equations
We consider the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance
Global weak solutions to the compressible quantum Navier–Stokes equation and its semi-classical limit
Abstract This paper is dedicated to the construction of global weak solutions to the quantum Navier–Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform
Energy equalities for compressible Navier–Stokes equations
The energy equalities of compressible Navier–Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient conditions on the
Energy conservation and Onsager's conjecture for the Euler equations
Onsager conjectured that weak solutions of the Euler equations for incompressible fluids in conserve energy only if they have a certain minimal smoothness (of the order of 1/3 fractional derivatives)
...
1
2
3
4
...