Restart of the global real mild trajectory #
The global regularized mild curve satisfies the same mild equation when viewed from any nonnegative start time.
theorem
CKN.Leray.regularizedGlobalMildCurve_shift_isTrajectory
(ρ : RegMollifierProfile)
(ε : ℝ)
(hε : 0 < ε)
(b₀ : ↥RealVectorL2)
(hbJ : RegularizedMildJData b₀)
(a T : ℝ)
(ha : 0 ≤ a)
(hT : 0 ≤ T)
:
IsRegularizedMildTrajectory ρ ε hε (regularizedGlobalMildCurve ρ ε hε b₀ hbJ a) T
(regularizedGlobalMildCurveShiftPath ρ ε hε b₀ hbJ a T)
The global mild curve restricted after a nonnegative start time is a mild trajectory with its state at that time as initial datum.