Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911776447135744 |
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| author | Diebou, Gael Y. |
| author_facet | Diebou, Gael Y. |
| contents | We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in homogenous Sobolev space with $s=-\frac{1}{2}$ degree of smoothness. Moreover, the velocity field is shown to be locally Hölder continuous while the pressure belongs to $L^p_{loc}$ for any $p\in (1,\infty)$. Our approach is based on the analysis of the inhomogeneous Stokes system for which we derive a new solvability result involving Dirichlet data in Triebel-Lizorkin classes with negative amount of smoothness and is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13719 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data Diebou, Gael Y. Analysis of PDEs We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in homogenous Sobolev space with $s=-\frac{1}{2}$ degree of smoothness. Moreover, the velocity field is shown to be locally Hölder continuous while the pressure belongs to $L^p_{loc}$ for any $p\in (1,\infty)$. Our approach is based on the analysis of the inhomogeneous Stokes system for which we derive a new solvability result involving Dirichlet data in Triebel-Lizorkin classes with negative amount of smoothness and is of independent interest. |
| title | Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.13719 |