Global motions for nonhomogeneous Navier-Stokes equations with large flux
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911772841082880 |
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| author | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| author_facet | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| contents | The nonhomogeneous Navier-Stokes equations are considered in a cylindrical domain in ${\mathbb R}^3$, parallel to the $x_3$-axis with large inflow and outflow on the top and the bottom. Moreover, on the lateral part of the cylinder the slip boundary conditions are assumed. The global existence of regular solutions is proved under assumptions that inflow and outflow are close to homogeneous and norms of derivative with respect to $x_3$ of the external force and initial velocity are sufficiently small. The key point of this paper is to verify that $x_3$-coordinate of velocity remains positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global motions for nonhomogeneous Navier-Stokes equations with large flux Rencławowicz, Joanna Zajączkowski, Wojciech M. Analysis of PDEs 35Q30, 76D03, 76D05 The nonhomogeneous Navier-Stokes equations are considered in a cylindrical domain in ${\mathbb R}^3$, parallel to the $x_3$-axis with large inflow and outflow on the top and the bottom. Moreover, on the lateral part of the cylinder the slip boundary conditions are assumed. The global existence of regular solutions is proved under assumptions that inflow and outflow are close to homogeneous and norms of derivative with respect to $x_3$ of the external force and initial velocity are sufficiently small. The key point of this paper is to verify that $x_3$-coordinate of velocity remains positive. |
| title | Global motions for nonhomogeneous Navier-Stokes equations with large flux |
| topic | Analysis of PDEs 35Q30, 76D03, 76D05 |
| url | https://arxiv.org/abs/2402.04793 |