Existence of smooth solutions of Navier-Stokes equations in 3D Euclidean space

3 months ago 1

[Submitted on 24 Jul 2025]

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 $\mathbb{R}^3$ by showing the existence and uniqueness of smooth solutions of the parabolic inertia Lamé equations and by letting a Lamé constant $\lambda$ tends to infinity (the other Lamé constant $\mu>0$ is fixed).