{"id":"openai-math/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation","pdf":"https://github.com/openai/math/blob/main/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equation-September-23-2026","tags":["kinetic-theory","boltzmann-equation","pde","analysis"],"score":0,"title":"Nonuniqueness for the periodic hard-sphere Boltzmann equation","domain":"Partial differential equations","family":"363","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"We prove nonuniqueness for the periodic hard-sphere Boltzmann equation by constructing two distinct global renormalized solutions with the same nonnegative initial density on $`\\mathbb T^3\\times\\mathbb R^3`$. This density has bounded velocity support and finite mass, energy, and absolute entropy. Both solutions conserve local mass and total momentum and satisfy the global energy and entropy-dissipation inequalities. On a common initial interval, they are strongly continuous in L 1 , and their collision gains and losses are integrable.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Nonuniqueness with local conservation for the hard-sphere Boltzmann equation"}