Global endpoint regularity #
The public theorem exposes the completed endpoint regularity result.
theorem
ESS.essGlobal
(T : ℝ)
(a : CKN.Foundation.Parabolic.Vec3 → CKN.Foundation.Parabolic.Vec3)
(u : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3)
(Du : CKN.Foundation.Parabolic.ParabolicPoint → Fin 3 → CKN.Foundation.Parabolic.Vec3)
:
CKN.IsLerayHopfSolution T a u Du →
essSup
(fun (t : ℝ) =>
∫⁻ (x : CKN.Foundation.Parabolic.Vec3), ENNReal.ofReal (CKN.Foundation.Parabolic.vec3EuclideanNorm (u (x, t))) ^ 3)
(MeasureTheory.volume.restrict (Set.Ioo 0 T)) < ⊤ →
CKN.SingularSet Set.univ (Set.Ioo 0 T) u = ∅
The global Escauriaza–Seregin–Šverák regularity theorem thm:ess-global.