Math models for how water flows only actually work if you assume nothing in the universe can ever travel faster than the speed of light.
March 27, 2026
Original Paper
The Spatial Hydrodynamic Attractor: Resurgence of the Gradient Expansion
arXiv · 2603.24611
The Takeaway
Standard fluid dynamics equations often produce 'infinite' errors that have puzzled physicists for years. Researchers found that enforcing the cosmic speed limit—a rule usually reserved for stars and atoms—actually forces these chaotic equations to settle down and provide clear, convergent answers, even in everyday fluid models.
From the abstract
Far-from-equilibrium kinetic systems collapse onto a hydrodynamic attractor, traditionally approximated by a gradient expansion. While temporal gradient series are non-Borel summable and require transseries completions, the analytic structure of the spatial expansion has remained elusive. Here, we derive exact closed-form Chapman--Enskog coefficients at all orders via Lagrange inversion and prove that the non-relativistic spatial gradient series, though factorially divergent, is strictly Borel s