Infinite velocity and vorticity have been proven to emerge from perfectly smooth water-like flow in a wide-open space.
The question of whether smooth initial conditions in fluid dynamics can lead to a singularity is one of the deepest unsolved problems in math. This paper demonstrates a mechanism for this blow-up to happen in the interior of a 3D fluid. It uses a specific quadrupole structure to drive the fluid toward an infinite collapse. This discovery overturns a long-held hope that fluid systems would stay smooth and predictable away from boundaries. It implies that turbulence might contain hidden points of infinite energy density. This changes the way we look at the most violent movements in nature.
Euler Singularities II: Interior Quadrupole Blow-Up for Smooth Axisymmetric Euler with Swirl in R3
arXiv · 2605.04526
We present a self-contained interior quadrupole mechanism for finite-time singularity formation in the axisymmetric three-dimensional incompressible Euler equations with swirl in the whole space. The construction is localized away from the axis. In local variables \[x=r-r_*(t),\qquad y=z, \] centered at a tracked radial point, the active vorticity and swirl profiles are \[G(x,y,t)\approx a(t)xy,\qquad\Gamma(x,y,t)\approx \Gamma_*(t)+\frac12 b(t)xy^2,\qquad \Gamma_*(t)>0. \] The first profile pro