论文标题
流体和气体流动的差异不变性
Differential invariants for flows of fluids and gases
论文作者
论文摘要
本文调查了作者在先前的论文中发现的结果（例如，请参见A. Duyunova，V。Lychagin，S。Tychkov，tychkov的差异，用于粘性液体的球形层流差异，几何学和物理学杂志，130，288-292（2018）的基础性和分类的层次化量和分类的层次化。流体力学，包括在平面上的Euler和Navier-Stokes方程，三维空间，一个球体和球形层。在每种情况下，都会发现对称性谎言代数，其次是对组动作的生成差异不变性和不变派的列表。主要扩展是对热力学状态，对称性和差异不变的详细分析。该分析是基于对Riemannian结构的考虑，自然与代表热力学状态的拉格朗日歧管相关。这种方法从根本上改变了对称代数的热力学部分以及差异不变的场的描述。
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130, 288-292 (2018)) concerning calculation and classification of symmetry Lie algebra and differential invariants for a variety of fundamental systems in fluid mechanics, including the Euler and Navier-Stokes equations on a plane, three-dimensional space, a sphere, and a spherical layer. In each case, the symmetry Lie algebra is found, followed by a list of generating differential invariants and invariant derivations for the group action. The main extension is a detailed analysis of thermodynamic states, symmetries, and differential invariants. This analysis is based on consideration of Riemannian structure naturally associated with Lagrangian manifolds that represent thermodynamic states. This approach radically changes the description of the thermodynamic part of the symmetry algebra as well as the field of differential invariants.
