  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.
