Vanishing of the zero-force pressure #
The force pressure in the forced regularized momentum identity vanishes on almost every slice when the force is zero.
theorem
CKN.Leray.forcePressure_zero_ae_on_interval
(T : ℝ)
(hT : 0 < T)
:
∀ᵐ (t : ℝ) ∂MeasureTheory.volume.restrict (Set.Ioo 0 T), (fun (x : Foundation.Parabolic.Vec3) =>
forcePressure (fun (x : Foundation.Parabolic.ParabolicPoint) => 0) isLocallySquareIntegrableForce_zero
(x, t)) =ᵐ[MeasureTheory.volume]
0
For zero forcing, the canonical force pressure is zero almost everywhere on every finite positive-time interval.