论文标题
径向可压缩流体流量和n> 1维度的气体动力学的对称性和卡西米尔
Symmetries and Casimirs of radial compressible fluid flow and gas dynamics in n>1 dimensions
论文作者
论文摘要
研究了n> 1个尺寸的径向可压缩流体流动的哈密顿方程的对称性和casimirs。进行了所有谎言点对称性的明确确定，从中获得了所有最大谎言对称代数的完整分类。该分类包括仅适用于特殊状态方程的所有谎言点对称性。对于一般的国家方程式，在最近的工作中发现的保守积分的层次结构被证明由汉密尔顿卡西米尔人组成。明确显示出仅适用于状态的熵方程的第二个层次结构，该层次结构包括非casimirs，通过径向流体流的方程式的汉密尔顿结构产生广义对称性的相应层次结构。一阶对称性显示出生成非亚伯利亚谎言代数。同样，在最近的工作中发现的两个新的运动保守积分也被证明可以产生用于状态和状态的熵方程的额外的一阶广义对称性。这些对称性产生了作用于流体方程溶液的明确转化组。由于众所周知，这些方程等于气体动力学方程，因此对于N维径向流体流量获得的所有结果都将延伸到径向气体动力学。
Symmetries and Casimirs are studied for the Hamiltonian equations of radial compressible fluid flow in n>1 dimensions. An explicit determination of all Lie point symmetries is carried out, from which a complete classification of all maximal Lie symmetry algebras is obtained. The classification includes all Lie point symmetries that exist only for special equations of state. For a general equation of state, the hierarchy of advected conserved integrals found in recent work is proved to consist of Hamiltonian Casimirs. A second hierarchy that holds only for an entropic equation of state is explicitly shown to comprise non-Casimirs which yield a corresponding hierarchy of generalized symmetries through the Hamiltonian structure of the equations of radial fluid flow. The first-order symmetries are shown to generate a non-abelian Lie algebra. Two new kinematic conserved integrals found in recent work are likewise shown to yield additional first-order generalized symmetries holding for a barotropic equation of state and an entropic equation of state. These symmetries produce an explicit transformation group acting on solutions of the fluid equations. Since these equations are well known to be equivalent to the equations of gas dynamics, all of the results obtained for n-dimensional radial fluid flow carry over to radial gas dynamics.
