Energy Conservation for the Weak Solutions of the Compressible Navier–Stokes Equations
Energy Conservation for the Weak Solutions of the Compressible Navier–Stokes Equations
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DOI：
10.1007/s00205-017-1121-4
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发表时间：
2016-05
影响因子：
2.5
通讯作者：
Cheng Yu
中科院分区：
文献类型：
--
作者：
Cheng Yu
在本文中，我们证明了在一定条件下，可压缩的N-S方程的弱解在一定条件下是守恒的。所得结果适用于常粘性方程的重整化解和退化粘性方程的弱解。我们的条件并不取决于维度。对于常粘性的可压缩N-S方程，能量可以在真空中守恒。我们的结果是关于可压缩N-S方程弱解的能量守恒的第一个结果。
In this paper, we prove the energy conservation for the weak solutions of the compressible Navier–Stokes equations for any timet> 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.