Self-dual solution of 3D incompressible Navier-Stokes equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913304554766336 |
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| author | Lai, Ning-An Zhou, Yi |
| author_facet | Lai, Ning-An Zhou, Yi |
| contents | Whether the 3D incompressible Navier-Stokes equations will have a global smooth solution for all smooth, finite energy initial data is a Millennium Prize problem. One of the main difficulties of this problem is that the Navier-Stokes equations are actually a system of semilinear heat equations rather than a single equation. In this paper, we discover a remarkable hidden symmetry of the 3D incompressible Navier-Stokes equations. Under this symmetric reduction, the system reduces to a single scalar semilinear heat equation. The symmetry also holds for the 3D incompressible Euler equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-dual solution of 3D incompressible Navier-Stokes equations Lai, Ning-An Zhou, Yi Analysis of PDEs Whether the 3D incompressible Navier-Stokes equations will have a global smooth solution for all smooth, finite energy initial data is a Millennium Prize problem. One of the main difficulties of this problem is that the Navier-Stokes equations are actually a system of semilinear heat equations rather than a single equation. In this paper, we discover a remarkable hidden symmetry of the 3D incompressible Navier-Stokes equations. Under this symmetric reduction, the system reduces to a single scalar semilinear heat equation. The symmetry also holds for the 3D incompressible Euler equations. |
| title | Self-dual solution of 3D incompressible Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.16642 |