一维可压缩Navier-Stokes方程组弱解的能量守恒

Energy conservation for the weak solutions of 1D the compressible Navier-Stokes equations

本文主要研究的是对任意的t>0,一维周期区域中可压缩Navier-Stokes方程组的弱解在某种特定的条件下满足能量守恒.具体来说,通过运用交换子估计的方法以及使弱解满足某种足够的正则性条件,从而可以得到在一维周期区域中弱解满足相应的能量等式.

In this paper,we study that the weak solutions of the compressible Navier-Stokes equations in the one-dimensional periodic region satisfy the conservation of energy under certain conditions for any time t>0 in one dimension.Precisely,by using commutator estimates theory and satisfying enough regularity conditions for weak solutions,we can obtain the corresponding energy equality of the weak solutions in the one-dimensional periodic region.