论文标题
稳定的轴对称无粘性流动的自由边界，涡度I：靠近退化点
The free boundary of steady axisymmetric inviscid flow with vorticity I: near the degenerate point
论文作者
论文摘要
在本文中，我们研究了稳定轴对称流的退化点附近的奇异性，其一般涡度不可压缩流体的一般涡度作用于重力和自由表面。我们调用了自由边界上的点，即流函数的梯度随着归化点而消失。本文的主要结果给出了自由表面上归化点附近的奇异性的不同分类。更确切地说，我们获得的是，在停滞点，可能的轮廓必须是stokes角，水平尖或水平平坦度。在对称轴上的简并点，除原点外，波轮廓必须是尖端。在原点上，可能的波轮廓必须是Garabedian尖的气泡，水平尖或水平平坦。
In this paper, we investigate the singularity near the degenerate points of the steady axisymmetric flow with general vorticity of an inviscid incompressible fluid acted on by gravity and with a free surface. We called the points on the free boundary at which the gradient of the stream function vanishes as the degenerate points. The main results in this paper give the different classifications of the singularity near the degenerate points on the free surface. More precisely, we obtained that at the stagnation points, the possible profiles must be a Stokes corner, or a horizontal cusp, or a horizontal flatness. At the degenerate points on the symmetric axis except the origin, the wave profile must be a cusp. At the origin, the possible wave profiles must be a Garabedian pointed bubble, or a horizontal cusp, or a horizontal flatness.
