论文标题
理想不可压缩的流体的稳定流动
Steady flows of ideal incompressible fluid
论文作者
论文摘要
建立了流体力学和差异几何形状之间的新重要关系。我们研究了具有附加特性的Euler方程的平滑稳定解：速度向量在任何时候都与压力的梯度正交。这样的解决方案称为加夫里洛夫流动。加夫里洛夫流的局部结构是用同位超曲面的几何形状来描述的。在3D情况下，我们获得了一个用于轴对称性Gavrilov流量的PDE系统，并找到了系统的一致性条件。提出了两个数字示例的轴对称性加夫里洛夫流量：轴向函数周期性沿轴向方向进行周期性，以及同等学上的表面差异为圆环。
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the pressure at any point. Such solutions are called Gavrilov flows. Local structure of a Gavrilov flow is described in terms of geometry of isobaric hypersurfaces. In the 3D case, we obtain a system of PDEs for an axisymmetric Gavrilov flow and find consistency conditions for the system. Two numerical examples of axisymmetric Gavrilov flows are presented: with pressure function periodic in the axial direction, and with isobaric surfaces diffeomorphic to the torus.
