The proved raw-field contract of the concrete admissible mean solver.
theorem
EulerMeanPacketProvider.meanSolve_angle_independent
(D : Data)
(raw : EulerPacketProfileRecursion.VectorField)
(h : Nonempty (Forcing D raw))
(t : ℝ)
(x : EulerSmoothLimit.Space)
(θ η : ℝ)
:
theorem
EulerMeanPacketProvider.meanSolve_divergence
(D : Data)
(raw : EulerPacketProfileRecursion.VectorField)
(h : Nonempty (Forcing D raw))
(t : ↑(Set.Icc 0 D.T))
(x : EulerSmoothLimit.Space)
(θ : ℝ)
:
EulerSmoothLimit.divergence
(fun (y : EulerSmoothLimit.Space) => (D.inverseFrame (↑t, y, θ)) ((meanSolve D raw).1 (↑t, y, θ))) x = 0
theorem
EulerMeanPacketProvider.meanSolve_initial_compact
(D : Data)
(raw : EulerPacketProfileRecursion.VectorField)
(h : Nonempty (Forcing D raw))
(θ : ℝ)
:
HasCompactSupport fun (x : EulerSmoothLimit.Space) => (meanSolve D raw).1 (0, x, θ)
theorem
EulerMeanPacketProvider.meanSolve_joint_continuous
(D : Data)
(raw : EulerPacketProfileRecursion.VectorField)
(h : Nonempty (Forcing D raw))
:
theorem
EulerMeanPacketProvider.meanSolve_angle_jets
(D : Data)
(raw : EulerPacketProfileRecursion.VectorField)
(h : Nonempty (Forcing D raw))
(t : ℝ)
(x : EulerSmoothLimit.Space)
(θ : ℝ)
:
(EulerPacketPointJets.slicedJet (Set.Icc 0 D.T) (meanSolve D raw).1 (t, x, θ)).2 EulerPacketPointJets.angleDirection = 0 ∧ (EulerPacketPointJets.pressureJet (meanSolve D raw).2 (t, x, θ)).2 EulerPacketPointJets.angleDirection = 0