Global-in-Time solutions of the Navier-Stokes equations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866915209534242816 |
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| author | Jennings, Gray |
| author_facet | Jennings, Gray |
| contents | We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $ when the viscosity $ ν$ is $ > 0 $. Such $ C^\infty $ solution of the Navier-Stokes equations are a solution of Option A of the Millenium Prize Problem of the Clay Institute for the Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_08270 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Global-in-Time solutions of the Navier-Stokes equations Jennings, Gray General Mathematics We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $ when the viscosity $ ν$ is $ > 0 $. Such $ C^\infty $ solution of the Navier-Stokes equations are a solution of Option A of the Millenium Prize Problem of the Clay Institute for the Navier-Stokes equations. |
| title | Global-in-Time solutions of the Navier-Stokes equations |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2002.08270 |