论文标题
开放问题中的几何流体动力学
Geometric Hydrodynamics in Open Problems
论文作者
论文摘要
自1966年著名的V. Arnold论文以来，几何流体动力学就一直蓬勃发展。在本文中，我们介绍了一系列开放问题，以及流体动力学的几种新结构以及对该领域的最新发展和成就的简洁调查。讨论的主题包括不同类型流体的变化设置，不变指标的模型，库奇和边界价值问题，对欧拉方程的解决方案的部分分析性，稳定而奇异的涡流解决方案，差异和差异和哈密顿的几何形状，差异群体的差异群体，长期的流体行为，以及直接的cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc cascc castcc castcc castcc cast的castcccccccccccccc cast cast的castcccccccccc均为iNNACCAD。
Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent developments and achievements in this area. The topics discussed include variational settings for different types of fluids, models for invariant metrics, the Cauchy and boundary value problems, partial analyticity of solutions to the Euler equations, their steady and singular vorticity solutions, differential and Hamiltonian geometry of diffeomorphism groups, long-time behaviour of fluids, as well as mechanical models of direct and inverse cascades.
