The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We derive a formulation of the dynamics of the vorticity Fourier modes on a periodic domain and ...

The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — until a new breakthrough result.

In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate ...