The old-corrector time term and old pressure term use the same fixed coefficient budget.
theorem
EulerPacketCylinderField.CoefficientBudget.slowCost_le
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
:
theorem
EulerPacketCylinderField.CoefficientBudget.fastCost_le
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
:
theorem
EulerPacketCylinderField.CoefficientBudget.linearCost_le
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
:
theorem
EulerPacketCylinderField.CoefficientBudget.multiplierCost_le
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
:
theorem
EulerPacketCylinderField.CoefficientBudget.previousLinear_bound
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
(hT : 0 < T)
(S : EulerPacketTimeProfile.Scales ↑(Set.Icc 0 T))
(p : ℕ)
(b : C(↑(Set.Icc 0 T), ℝ))
(hb : ∀ (t : ↑(Set.Icc 0 T)), 0 < b t)
{raw raw_t : EulerPacketProfileRecursion.VectorField}
(G : Field P T raw)
(H : Field P T raw_t)
(htime : TimeDerivative ⋯ G H)
{R : ℝ}
(hG : (G.normalized ⋯ (S.high (p - 1)) ⋯).WordBound 6 R 1 (EulerPacketShiftArithmetic.highShift (p - 1)))
(hH : (H.normalized ⋯ (S.high (p - 1)) ⋯).WordBound 6 R 1 (EulerPacketShiftArithmetic.highShift (p - 1)))
(hRc : EulerParameterWordGevrey.sobolevCoefficientRadius (Fin 4) B.Rc ≤ R)
(hprofile : ∀ (t : ↑(Set.Icc 0 T)), (S.high (p - 1)) t ≤ b t)
:
((Field.linearPart C.strain G H hT htime O.interval ⋯).normalized ⋯ b hb).WordBound 6 R B.linearCost
(EulerPacketShiftArithmetic.highShift (p - 1))
theorem
EulerPacketCylinderField.CoefficientBudget.previousPressure_bound
{P T : ℝ}
[Fact (0 < P)]
{O : EulerPacketProfileRecursion.Operators}
{C : CoefficientData P T O}
(B : CoefficientBudget C)
(hT : 0 < T)
(S : EulerPacketTimeProfile.Scales ↑(Set.Icc 0 T))
(p : ℕ)
(b : C(↑(Set.Icc 0 T), ℝ))
(hb : ∀ (t : ↑(Set.Icc 0 T)), 0 < b t)
(q : EulerPacketProfileRecursion.ScalarField)
(G : Field P T (pressureGradient q))
{R : ℝ}
(hG : (G.normalized ⋯ (S.high (p - 1)) ⋯).WordBound 6 R 1 (EulerPacketShiftArithmetic.highShift (p - 1)))
(hRc : EulerParameterWordGevrey.sobolevCoefficientRadius (Fin 4) B.Rc ≤ R)
(hprofile : ∀ (t : ↑(Set.Icc 0 T)), (S.high (p - 1)) t ≤ b t)
:
((Field.slowPressure C.inverse q G).normalized ⋯ b hb).WordBound 6 R B.multiplierCost
(EulerPacketShiftArithmetic.highShift (p - 1))