Blowup Pressure Bound

Pressure bounds and convergence estimates for the rescaled sequence.

theorem ESS.blowup_rescaled_pressureSlice_eLpNorm_threeHalves_eq (f : CKN.Foundation.Parabolic.Vec3 → ℝ) (hf : MeasureTheory.AEStronglyMeasurable f MeasureTheory.volume) (x₀ : CKN.Foundation.Parabolic.Vec3) (r : ℝ) (hr : 0 < r) : MeasureTheory.eLpNorm (fun (x : CKN.Foundation.Parabolic.Vec3) => r ^ 2 * f (x₀ + r • x)) (3 / 2) MeasureTheory.volume = MeasureTheory.eLpNorm f (3 / 2) MeasureTheory.volume

The global L^(3/2) pressure norm is invariant under positive spatial Navier–Stokes rescaling.