论文标题
在稳定的轴对称涡旋环上，用于3-D不可压缩的Euler流动
On the steady axisymmetric vortex rings for 3-D incompressible Euler flows
论文作者
论文摘要
在本文中，我们研究了三维不可压缩的欧拉流的稳定涡流环的非线性降低。我们构建了一个稳定的涡流环（带有和不旋转）的家族，该家族构成了$ \ Mathbb {r}^3 $中经典的圆形涡旋细丝的降低。该构建基于对临床椭圆问题的解决方案的研究\ begin {equation*} - \ frac {1} {r} {r} \ frac {\ partial} {\ partial r} \ big（\ big big（\ frac {1}} r} \ big） - \ frac {1} {r^2} \ frac {\ partial^2ψ^\ varepsilon} {\ partial z^2} = \ frac {1} {\ varepsilon^2} \ left（g（ψ^^\ varepsilon）+\ frac {f（ψ^\ varepsilon）} {r^2} \ right） $ψ^\ varepsilon $，$ \ varepsilon> 0 $是一个小参数。
In this paper, we study nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler flows. We construct a family of steady vortex rings (with and without swirl) which constitutes a desingularization of the classical circular vortex filament in $\mathbb{R}^3$. The construction is based on a study of solutions to the similinear elliptic problem \begin{equation*} -\frac{1}{r}\frac{\partial}{\partial r}\Big(\frac{1}{r}\frac{\partialψ^\varepsilon}{\partial r}\Big)-\frac{1}{r^2}\frac{\partial^2ψ^\varepsilon}{\partial z^2}=\frac{1}{\varepsilon^2}\left(g(ψ^\varepsilon)+\frac{f(ψ^\varepsilon)}{r^2}\right), \end{equation*} where $f$ and $g$ are two given functions of the Stokes stream function $ψ^\varepsilon$, and $\varepsilon>0$ is a small parameter.
