Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917027823747072 |
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| author | Liu, Genqian |
| author_facet | Liu, Genqian |
| contents | 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 $λ$ tends to infinity (the other Lamé constant $μ>0$ is fixed). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space Liu, Genqian Analysis of PDEs Mathematical Physics 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 $λ$ tends to infinity (the other Lamé constant $μ>0$ is fixed). |
| title | Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2507.18063 |