Initial value of the linear complete Sobolev mild map

The prescribed physical coefficient does not alter the initial state of the complete Sobolev mild equation.

theorem CKN.Leray.regularisedBesselLinearLocalMap_zero (ρ : RegMollifierProfile) (ε : ℝ) (hε : 0 < ε) (k : ℕ) (b : BesselPotentialSpace Foundation.Parabolic.L2Vec3 ComplexVec3 (↑(2 * k)) 2) (T : ℝ) (hT : 0 ≤ T) (g : C(↑(RegularizedMildTimeInterval T), ↥ComplexVectorL2)) (B : ℝ) (hB : 0 ≤ B) (hg : ∀ (q : ↑(RegularizedMildTimeInterval T)), ‖g q‖ ≤ B) (v : C(↑(RegularizedMildTimeInterval T), BesselPotentialSpace Foundation.Parabolic.L2Vec3 ComplexVec3 (↑(2 * k)) 2)) : (regularisedBesselLinearLocalMap ρ ε hε k b T hT g B hB hg v) ⟨0, ⋯⟩ = b

Every image of the linear complete Sobolev mild map takes its prescribed complete Sobolev initial datum at time zero.