{"id":"openai-math/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals","pdf":"https://github.com/openai/math/blob/main/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Boltzmann-Grad-limit-for-stable-radial-potentials-on-regular-kinetic-intervals-September-23-2026","tags":["kinetic-theory","boltzmann-equation","mathematical-physics"],"score":0,"title":"The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals","domain":"Partial differential equations","family":"364","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We derive the nonlinear Boltzmann equation from a grand-canonical Newtonian gas with initial pair exclusion. We treat stable, finite-range radial potentials that are C 2 except for an allowed repulsive singularity at the origin, and C 1 initial probability densities with spatially summable Gaussian bounds on the density and its spatial gradient. All fixed-order rescaled factorial marginals converge in L 1 , uniformly throughout every finite interval on which the classical kinetic solution has a uniform Gaussian bound. The result allows attractive wells and dynamically formed clusters,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Kinetic limits and fluctuations over the Boltzmann lifespan"}