Blowup Suitable Integrable

Integrability conditions needed for suitability of the rescaled fields.

theorem ESS.blowupRescale_eventually_suitableIntegrable_outer (u : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3) (Du : CKN.Foundation.Parabolic.ParabolicPoint → Fin 3 → CKN.Foundation.Parabolic.Vec3) (p : CKN.Foundation.Parabolic.ParabolicPoint → ℝ) (hSuitable : CKN.IsSuitableWeakSolution (CKN.Foundation.Parabolic.vec3Ball 0 (3 / 4)) (Set.Ioo (-1) 0) 3 u Du p 0) (x₀ : CKN.Foundation.Parabolic.Vec3) (t₀ : ℝ) (r : ℕ → ℝ) (hx₀ : x₀ ∈ closure (CKN.Foundation.Parabolic.vec3Ball 0 (1 / 2))) (ht₀ : t₀ ∈ Set.Icc (-(1 / 4)) 0) (hr : ∀ (k : ℕ), 0 < r k) (hr0 : Filter.Tendsto r Filter.atTop (nhds 0)) (R a : ℝ) (hR : 0 < R) (ha : a < 0) : ∀ᶠ (k : ℕ) in Filter.atTop, CKN.IsSuitableWeakSolutionIntegrable (CKN.euclideanBall 0 (R + 1)) (Set.Ioo (a - 2) 0) 3 (parabolicRescaleVelocity x₀ t₀ (r k) u) (parabolicRescaleGradient x₀ t₀ (r k) Du) (parabolicRescalePressure x₀ t₀ (r k) p) 0

The rescaled solutions satisfy the integrable suitable class on each fixed larger past cylinder once the scale is small.