All open problems
Source labels openChecked July 26, 2026
Millennium ProblemsPartial differential equations
Existence And Smoothness Of The Navier–Stokes Equation
(A) Existence and smoothness of Navier–Stokes solutions on ℝ³.
Mathematical statement
(A) Existence and smoothness of Navier–Stokes solutions on ℝ³.
Statement source: Millennium Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
navier_stokes_existence_and_smoothness_R3
Complete statement target, proof intentionally absentLean 4
theorem navier_stokes_existence_and_smoothness_R3 (nu : ℝ) (hnu : nu > 0) (u₀ : ℝ³ → ℝ³) (hu₀ : InitialVelocityConditionDecay u₀) : ∃ v p, NavierStokesExistenceAndSmoothnessRn nu u₀ (f := 0) v p := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References