def
definition
def or abbrev
IsNSDuhamelTraj
show as:
view Lean formalization →
formal statement (Lean)
194def IsNSDuhamelTraj (ν : ℝ) (D : ℝ → FourierState2D) (u : ℝ → FourierState2D) : Prop :=
proof body
Definition body.
195 ∀ t ≥ 0, ∀ k : Mode2, (u t) k = (heatFactor ν t k) • (u 0) k + (D t) k
196
197namespace IsStokesMildTraj
198
199/-- Mild Stokes/heat identity implies the corresponding differential equation (within `t ≥ 0`). -/
used by (10)
-
nsDuhamelCoeffBound -
nsDuhamelCoeffBound_kernelIntegral -
nsDuhamelCoeffBound_kernelIntegral_of_forcing -
nsDuhamel_of_forall -
nsDuhamel_of_forall_kernelIntegral -
nsDuhamel_of_forall_kernelIntegral_of_forcing -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcing -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcingHyp