Spatial decay/asymptotics in the Navier-Stokes equation
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916440025595904 |
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| author | Topalov, Peter |
| author_facet | Topalov, Peter |
| contents | We discuss the appearance of spatial asymptotic expansions of solutions of the Navier-Stokes equation on $\mathbb{R}^n$. In particular, we prove that the Navier-Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop non-trivial asymptotic terms as $|x|\to\infty$. In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spatial decay/asymptotics in the Navier-Stokes equation Topalov, Peter Analysis of PDEs We discuss the appearance of spatial asymptotic expansions of solutions of the Navier-Stokes equation on $\mathbb{R}^n$. In particular, we prove that the Navier-Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop non-trivial asymptotic terms as $|x|\to\infty$. In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion. |
| title | Spatial decay/asymptotics in the Navier-Stokes equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.11796 |