The three-dimensional periodic hard-sphere Boltzmann equation has one nonnegative initial density with bounded velocity support and finite mass, energy and absolute entropy that yields two distinct global entropy solutions, both satisfying exact local conservation of mass, momentum and kinetic energy and strong L¹ continuity.
The three-dimensional periodic hard-sphere Boltzmann equation has one nonnegative initial density with bounded velocity support and finite mass, energy and absolute entropy that yields two distinct global entropy solutions, both satisfying exact local conservation of mass, momentum and kinetic energy and strong L¹ continuity.
The three-dimensional periodic hard-sphere Boltzmann equation has one nonnegative initial density with bounded velocity support and finite mass, energy and absolute entropy that yields two distinct global entropy solutions, both satisfying exact local conservation of mass, momentum and kinetic energy and strong L¹ continuity.
If correct, shows that enforcing every local collision-invariant balance does not restore uniqueness.
Can exact local mass, momentum and energy conservation coexist with Boltzmann nonuniqueness?
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OpenAI reports Boltzmann nonuniqueness with exact local conservation
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