The global estimate for regular axially-symmetric solutions to the Navier Stokes equations coupled with the heat conduction
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912210971787264 |
|---|---|
| author | Grygierzec, Wiesław J. Zajączkowski, Wojciech M. |
| author_facet | Grygierzec, Wiesław J. Zajączkowski, Wojciech M. |
| contents | The axially-symmetric solutions to the Navier-Stokes equations coupled with the heat conduction are considered. in a bounded cylinder $Ω\subset \mathbb{R}^3$. We assume that $v_r, v_φ, ω_φ$ vanish on the lateral part $S_1$ of the boundary $\partial Ω$ and $v_z, ω_φ, \partial_z v_φ$ vanish on the top and bottom of the cylinder, where we used standard cylindrical coordinates and $ω=\text{rot} v$ is the vorticity of the fluid. Moreover, vanishing of the heat flux through the boundary is imposed. Assuming existence of a sufficiently regular solution we derive a global a priori estimate in terms of data. The estimate is such that a global regular solutions can be proved. We prove the estimate because some reduction of nonlinearity are found.Moreover, deriving the global estimate for a local solution implies a possibility of its extension in time as long as the estimate holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The global estimate for regular axially-symmetric solutions to the Navier Stokes equations coupled with the heat conduction Grygierzec, Wiesław J. Zajączkowski, Wojciech M. Analysis of PDEs Mathematical Physics 35A01, 35B01, 35B65, 35Q30, 76D03, 76D05 The axially-symmetric solutions to the Navier-Stokes equations coupled with the heat conduction are considered. in a bounded cylinder $Ω\subset \mathbb{R}^3$. We assume that $v_r, v_φ, ω_φ$ vanish on the lateral part $S_1$ of the boundary $\partial Ω$ and $v_z, ω_φ, \partial_z v_φ$ vanish on the top and bottom of the cylinder, where we used standard cylindrical coordinates and $ω=\text{rot} v$ is the vorticity of the fluid. Moreover, vanishing of the heat flux through the boundary is imposed. Assuming existence of a sufficiently regular solution we derive a global a priori estimate in terms of data. The estimate is such that a global regular solutions can be proved. We prove the estimate because some reduction of nonlinearity are found.Moreover, deriving the global estimate for a local solution implies a possibility of its extension in time as long as the estimate holds. |
| title | The global estimate for regular axially-symmetric solutions to the Navier Stokes equations coupled with the heat conduction |
| topic | Analysis of PDEs Mathematical Physics 35A01, 35B01, 35B65, 35Q30, 76D03, 76D05 |
| url | https://arxiv.org/abs/2501.18302 |