A rigid body moving through an ideal fluid is one of the oldest problems in mathematical physics. The fluid is incompressible, inviscid, two-dimensional. The body is a solid obstacle. What could go wrong?
Vorticity. The fluid's rotational content can concentrate, interact with the body, and potentially blow up in finite time. Previous global existence results required restrictive assumptions: the body had to be a disk, or the vorticity had to satisfy special conditions.
The authors (arXiv:2603.23087) prove global well-posedness for a rigid body of arbitrary shape in a 2D perfect fluid, removing both constraints. The key is establishing a Beale-Kato-Majda type bound — showing that the vorticity cannot concentrate faster than the energy allows, regardless of the body's geometry.
The through-claim: the shape of the obstacle is irrelevant to global existence. The previous restriction to disks wasn't capturing a physical obstruction but a mathematical convenience. The energy structure of the 2D fluid-body system prevents singularity formation for any shape, not because of symmetry but because of dimension.