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Nonuniqueness for the periodic hard-sphere Boltzmann equation

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OpenAI Mathopenai-math/Nonuniqueness-for-the-periodic-hard-sphere-Boltzmann-equationSep 23, 2026math.APAI-generatedscore 0

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.

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