Stability Slice Convergence

Supporting estimates for the Navier–Stokes development.

theorem CKN.stability_exists_subsequence_ae_slices_of_eLpNorm_tendsto {α : Type u_1} {β : Type u_2} {E : Type u_3} [MeasurableSpace α] [MeasurableSpace β] [NormedAddCommGroup E] (μ : MeasureTheory.Measure α) [MeasureTheory.SFinite μ] (ν : MeasureTheory.Measure β) (p : ENNReal) (hp : p ≠ 0) (F : ℕ → β × α → E) (G : β × α → E) (hconv : Filter.Tendsto (fun (n : ℕ) => MeasureTheory.eLpNorm (F n - G) p (ν.prod μ)) Filter.atTop (nhds 0)) : ∃ (σ : ℕ → ℕ), StrictMono σ ∧ ∀ᵐ (t : β) ∂ν, ∀ᵐ (x : α) ∂μ, Filter.Tendsto (fun (n : ℕ) => F (σ n) (t, x)) Filter.atTop (nhds (G (t, x)))

Strong space-time convergence has a subsequence converging on almost every spatial slice for almost every time (thm:stability).