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def definition def or abbrev

IsStokesMildTraj

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formal statement (Lean)

 164def IsStokesMildTraj (ν : ℝ) (u : ℝ → FourierState2D) : Prop :=

proof body

Definition body.

 165  ∀ t ≥ 0, ∀ k : Mode2, (u t) k = (heatFactor ν t k) • (u 0) k
 166
 167/-- Differential (within `t ≥ 0`) Stokes/heat equation in Fourier coefficients (modewise).
 168
 169This is a slightly more “PDE-like” statement than the mild form: for each fixed mode `k`,
 170the coefficient trajectory satisfies
 171
 172`d/dt u(t,k) = -(ν |k|^2) • u(t,k)`
 173
 174as a derivative **within** the half-line `[0,∞)`. -/

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