A legendary "impossible" math problem about how gases and stars collapse has finally been solved for 3D spheres.
April 14, 2026
Original Paper
Global existence of classical solutions for the multi-dimensional compressible Navier-Stokes-Poisson equations on solid balls for arbitrary spherically symmetric large initial data
arXiv · 2604.08946
The Takeaway
Mathematicians proved that stable solutions exist for massive, swirling fluids even with "large" starting data, which was a long-standing mystery. This provides a rock-solid foundation for understanding how stars and galactic gases behave without the math breaking down into nonsense.
From the abstract
Whether the 3D compressible Navier-Stokes-Poisson equations admit global classical solutions for general large initial data has long been a challenging open problem. In this paper, we provide an affirmative answer to this question under spherical symmetry on solid balls . Specifically, we consider the initial-boundary value problem for the multi-dimensional compressible equations with density-dependent viscosity coefficients satisfying the BD-type entropy equality, namely, assuming $\mu=\rho^{\a