On the Stokes system in cylindrical domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913225357918208 |
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| author | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| author_facet | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| contents | The existence of solutions to some initial-boundary value problem for the Stokes system is proved. The result is shown in Sobolev-Slobodetskii spaces such that the velocity belongs to $W_r^{2+σ,1+σ/2}(Ω^T)$ and gradient of pressure to $W_r^{σ,σ/2}(Ω^T)$, where $r\in(1,\infty)$, $σ\in(0,1)$, $Ω^T=Ω\times(0,T)$. These are special Besov spaces: $B_{r,r}^{2+σ,1+σ/2}(Ω^T)$ and $B_{r,r}^{σ,σ/2}(Ω^T)$, respectively. The existence is proved by the technique of regularizer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_08083 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the Stokes system in cylindrical domains Rencławowicz, Joanna Zajączkowski, Wojciech M. Analysis of PDEs Mathematical Physics 76D07 (Primary) 35Q35, 76N10 (Secondary) The existence of solutions to some initial-boundary value problem for the Stokes system is proved. The result is shown in Sobolev-Slobodetskii spaces such that the velocity belongs to $W_r^{2+σ,1+σ/2}(Ω^T)$ and gradient of pressure to $W_r^{σ,σ/2}(Ω^T)$, where $r\in(1,\infty)$, $σ\in(0,1)$, $Ω^T=Ω\times(0,T)$. These are special Besov spaces: $B_{r,r}^{2+σ,1+σ/2}(Ω^T)$ and $B_{r,r}^{σ,σ/2}(Ω^T)$, respectively. The existence is proved by the technique of regularizer. |
| title | On the Stokes system in cylindrical domains |
| topic | Analysis of PDEs Mathematical Physics 76D07 (Primary) 35Q35, 76N10 (Secondary) |
| url | https://arxiv.org/abs/2111.08083 |