Stability S2

Supporting estimates for the Navier–Stokes development.

theorem CKN.stability_suitable_divergence {Ω : Set Foundation.Parabolic.Vec3} {I : Set ℝ} {q : ℝ} (u : ℕ → Foundation.Parabolic.ParabolicPoint → Foundation.Parabolic.Vec3) (Du : ℕ → Foundation.Parabolic.ParabolicPoint → Fin 3 → Foundation.Parabolic.Vec3) (p : ℕ → Foundation.Parabolic.ParabolicPoint → ℝ) (v : Foundation.Parabolic.ParabolicPoint → Foundation.Parabolic.Vec3) (hsol : ∀ (n : ℕ), IsSuitableWeakSolution Ω I q (u n) (Du n) (p n) 0) (huConv : ∀ (Ω' : Set Foundation.Parabolic.Vec3) (J : Set ℝ), localBox Ω I Ω' J → Filter.Tendsto (fun (n : ℕ) => MeasureTheory.eLpNorm (u n - v) 3 (MeasureTheory.volume.restrict (spaceTimeSet Ω' J))) Filter.atTop (nhds 0)) (ψ : Foundation.Parabolic.Vec3 × ℝ → ℝ) : ψ ∈ spaceTimeTestFunction Ω I → ∫ (z : Foundation.Parabolic.ParabolicPoint) in spaceTimeSet Ω I, ∑ i : Fin 3, v z i * spatialPartial ψ i z = 0

The distributional divergence identity (S2) passes to the strong local L³ limit in thm:stability.