论文标题
希尔球形涡流的稳定性
Stability of Hill's spherical vortex
论文作者
论文摘要
我们研究了M. Hill在1894年引入的球形涡流的稳定性，这是三维不可压缩的Euler方程的明确解决方案。流动为对称，没有漩涡，涡流芯只是在恒定速度的对称轴上滑动的球，而核心的涡度与距离对称轴的距离成正比。我们使用A. Friedman和B. Turkington引入的变异设置（Trans。Amer。Math。Soc。，1981），该设置在涡旋强度，脉冲和循环的约束下产生了动能的最大化器。我们通过C. Amick和L. Fraenkel的独特性结果（Arch。Mech。Mech。Anal。，1986），将一组最大化器与山丘的涡流匹配。匹配过程是通过涡旋核心附近的近似值（所谓的度量边界点）来完成的。结果，使用浓缩的紧凑度方法获得了直至翻译的稳定性。
We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three-dimensional incompressible Euler equations. The flow is axi-symmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting introduced by A. Friedman and B. Turkington (Trans. Amer. Math. Soc., 1981), which produced a maximizer of the kinetic energy under constraints on vortex strength, impulse, and circulation. We match the set of maximizers with the Hill's vortex via the uniqueness result of C. Amick and L. Fraenkel (Arch. Rational Mech. Anal., 1986). The matching process is done by an approximation near exceptional points (so-called metrical boundary points) of the vortex core. As a consequence, the stability up to a translation is obtained by using a concentrated compactness method.
