Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 363-02. Nonuniqueness for the periodic hard-sphere Boltzmann equation
Manuscript map · lines 9365–9374
OpenAI@2026-10-07#rem:oai-p-363-02
Authors: OpenAI. Family 363.
Title: Nonuniqueness for the periodic hard-sphere Boltzmann equation.
Abstract: 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 L1, and their collision gains and losses are integrable.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- section: Manuscript map
- remark: Remark: 001-01. Milne's rationality conjecture for abelian varieties
- remark: Remark: 002-01. Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank
- remark: Remark: 002-02. The Selmer converse for elliptic curves at every prime
- remark: Remark: 002-03. The two-primary Birch–Swinnerton-Dyer formula in Selmer corank at most one
- remark: Remark: 003-01. The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane s 7/8
- remark: Remark: 003-02. The Quasi-Riemann Hypothesis (alternate 11/12 proof)
- remark: Remark: 003-03. Uniform exclusion of Landau–Siegel zeros