正压不可压缩流体无粘旋涡流动问题的陈述
Statement of problem on vortical inviscid flow of barotropic and incompressible fluids
摘要：
研究了确定理想流体的流体动力学方程的唯一解需要什么信息的问题。考虑正压流体和不可压缩流体的任意无粘流动。在对流体动力学方程进行积分之后，关于流体流动的所有信息以不定函数的形式集中在动力学方程中，而初始和边界条件包含关于流体颗粒标记的信息。本文指出，为了确定不可压缩流体的定常流动，必须给出任意流线上的涡量。给定边界上的速度，一般不能确定涡量.如果有闭合的流线，则不能通过边界条件给出其上的涡量。这种情况解释了在相同的边界条件下存在不同的定常涡流。
英文摘要：
The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the fluid flow is concentrated in dynamic equations in the form of indefinite functions, whereas the initial and boundary conditions contain information on the fluid particle labeling. It is shown that for determination of the stationary flow of the incompressible fluid the vorticity on any stream line must be given. Giving the velocity on the boundary, one does not determine the vorticity, in general. If there are closed stream lines, the vorticity cannot be given on them via boundary conditions. This circumstance explains existence of different stationary vortical flows under the same boundary conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
