| import OAI.MathematicalPhysics.Boltzmann.UnconditionalMainProof | |
| namespace OAI | |
| /-! # Nonuniqueness for the periodic hard-sphere Boltzmann equation | |
| The exact main statement includes two distinct global renormalized solutions of one | |
| bounded-velocity initial datum, with local mass conservation, total momentum conservation, energy and | |
| entropy-dissipation inequalities, and strong early L1 continuity with integrable collisions. | |
| -/ | |
| namespace BoltzmannNonuniqueness | |
| theorem nonuniqueness : | |
| ∃ f₀ : Density, BoundedVelocitySupport f₀ ∧ | |
| ∃ (F G : Evolution) (T : ℝ), AdmissibleGlobal f₀ F ∧ AdmissibleGlobal f₀ G ∧ | |
| StrongEarly T F ∧ StrongEarly T G ∧ | |
| ∃ t ∈ Set.Icc 0 T, ¬(F t =ᵐ[MeasureTheory.volume] G t) := | |
| nonuniqueness_proved | |
| end BoltzmannNonuniqueness | |
| end OAI | |