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caec230 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | import OAI.MathematicalPhysics.Transonic.Profile.Equations
namespace OAI
section
noncomputable section
open scoped ContDiff
namespace SepticProfile
def RelativisticProfileExists : Prop :=
∃ (beta : ℝ) (g : ℝ → ℝ),
1 < beta ∧ beta*(ell + Real.sqrt ell) < 3 ∧
ContDiffOn ℝ ∞ g (Set.Ici 0) ∧
let v : ℝ → ℝ := fun y => y*g (y^2)
(∀ y : ℝ, 0 ≤ y → |v y| < 1) ∧
(∀ y : ℝ, 0 ≤ y →
profileDenom ell y (v y) * deriv v y = profileNumer ell beta y (v y)) ∧
(∀ y : ℝ, 0 < y → v y < y ∧ y*v y < 1) ∧
0 < sonicRadius beta ∧ sonicRadius beta < 1 ∧
(∀ y : ℝ, 0 ≤ y →
(velocityToU y (v y) = sonicSpeed ↔ y = sonicRadius beta)) ∧
0 < deriv (fun y => velocityToU y (v y)) (sonicRadius beta)
end SepticProfile
end
end
end OAI
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