(hnu : 0 < nu) (f : Fin 3 → ℝ) : ∃ (T : UnboundedSelfAdjoint (L2I Vel)) (U : ℝ → (L2I Vel →L[ℂ] L2I Vel)), IsSelfAdjointExtension (lagrangianCore (lagCanData nu hnu f)) T.op ∧...

Proved

BookProof.NavierStokesFlow.LagrangianCanonical.lagCan_stone_flow

by leonardopedro · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.LagrangianCanonical.lagCan_stone_flow (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble

-- Generated from ChapterNavierStokesLagrangianCanonical.lean — theorem BookProof.NavierStokesFlow.LagrangianCanonical.lagCan_stone_flow
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianCanonical
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterStoneBridge
open BookProof.EsaClosure
open BookProof.ChapterStoneResolvent
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.LagrangianCanonical
















open scoped ENNReal



open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato  BookProof.NavierStokesFlow.LagrangianKatoRellich
open BookProof.NavierStokesFlow.CanonicalVector BookProof.NavierStokesFlow.ThreeComponent














variable (nu : ℝ)

open BookProof.NavierStokesFlow.LagrangianKatoRellich
open BookProof.ChapterStoneResolvent BookProof.StoneBridge BookProof.EsaClosure in

Formal statement

theorem BookProof.NavierStokesFlow.LagrangianCanonical.lagCan_stone_flow (hnu : 0 < nu) (f : Fin 3 → ℝ) :
    ∃ (T : UnboundedSelfAdjoint (L2I Vel)) (U : ℝ → (L2I Vel →L[ℂ] L2I Vel)),
      IsSelfAdjointExtension (lagrangianCore (lagCanData nu hnu f)) T.op ∧ IsStoneFlow T U := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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