The Boltzmann–Grad limit for stable radial potentials on regular kinetic intervals
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,…
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