Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space

2025/07/24 by Genqian Liu, Liu, Genqian · 2 voices
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP

paper · pdf · doi:10.48550/arxiv.2507.18063

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

Based on the essential connection of the parabolic inertia Lamé equations and Navier-Stokes equations, we prove the existence of smooth solutions of the incompressible Navier-Stokes equations in three-dimensional Euclidean space ℝ³ by showing the existence and uniqueness of smooth solutions of the parabolic inertia Lamé equations and by letting a Lamé constant λ tends to infinity (the other Lamé constant μ>0 is fixed).

Discussions

• A claim of smooth solutions to the Navier-Stokes equations: arxiv.org/pdf/2507.18063 If this holds, then another millenium problem is resolved! [bsky, 5 points, 0 comments]
• Existence of smooth solutions of Navier-Stokes equations in 3D Euclidean space [hn, 4 points, 0 comments]

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