On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918367924846592 |
|---|---|
| author | Hou, Hedong |
| author_facet | Hou, Hedong |
| contents | We prove that any mild solution in the Koch--Tataru space to the incompressible Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ is weak*-continuous in time, valued in $\mathrm{BMO}^{-1}$. We also show that the global mild solution vanishes in $\mathrm{BMO}^{-1}$ at infinity in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16468 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ Hou, Hedong Analysis of PDEs Classical Analysis and ODEs 35Q30, 42B37, 76D03 We prove that any mild solution in the Koch--Tataru space to the incompressible Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ is weak*-continuous in time, valued in $\mathrm{BMO}^{-1}$. We also show that the global mild solution vanishes in $\mathrm{BMO}^{-1}$ at infinity in time. |
| title | On regularity of solutions to the Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ |
| topic | Analysis of PDEs Classical Analysis and ODEs 35Q30, 42B37, 76D03 |
| url | https://arxiv.org/abs/2410.16468 |