论文标题
$ n> 1 $尺寸的新的保守积分和径向压缩流的不变性
New conserved integrals and invariants of radial compressible flow in $n>1$ dimensions
论文作者
论文摘要
研究了保守的积分和不变式（质量标量），以$ n> 1 $尺寸的径向压缩流体/气流方程。除了熵（这是一个众所周知的不变）外，还可以从对一阶的不变性的明确测定中发现另外三个不变。一个人持有国家的一般方程式，另外两个仅适用于国家熵方程。提出了一个不变的递归操作员，该运算符会产生两个高阶不变的层次结构。每个不变形都产生相应的积分不变式，描述了在运输的径向域上的保守积分。此外，对运动学保守密度的直接确定发现了两个“隐藏”的未经看见的保守积分：一个描述了焓升，用于状态的正压方程；另一个描述了熵加权的能量，为状态的熵方程提供。对一类一阶保守密度的进一步明确确定表明，在运输的径向域上的相应的非依赖性保守积分等同于积分不变的，模量琐事密度。
Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in $n>1$ dimensions. Apart from entropy, which is a well-know invariant, three additional invariants are found from an explicit determination of invariants up to first-order. One holds for a general equation of state, and the two others hold only for entropic equations of state. A recursion operator on invariants is presented, which produces two hierarchies of higher-order invariants. Each invariant yields a corresponding integral invariant, describing an advected conserved integral on transported radial domains. In addition, a direct determination of kinematic conserved densities uncovers two "hidden" non-advected conserved integrals: one describes enthalpy-flux, holding for barotropic equations of state; the other describes entropy-weighted energy, holding for entropic equations of state. A further explicit determination of a class of first-order conserved densities shows that the corresponding non-kinematic conserved integrals on transported radial domains are equivalent to integral invariants, modulo trivial densities.
