A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911345003200512 |
|---|---|
| author | Nguyen, Tien-Tai |
| author_facet | Nguyen, Tien-Tai |
| contents | In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the linearized equations is shown via the operator method of Lafitte and Nguyen (2022). Hence, we prove the nonlinear instability by adapting the framework of Desjardins and Grenier (2003) studying some classes of viscous boundary layers to obtain two separated solutions at escaping time. Our work performs a different approach from that of Ding, Li and Xin (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions Nguyen, Tien-Tai Analysis of PDEs In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the linearized equations is shown via the operator method of Lafitte and Nguyen (2022). Hence, we prove the nonlinear instability by adapting the framework of Desjardins and Grenier (2003) studying some classes of viscous boundary layers to obtain two separated solutions at escaping time. Our work performs a different approach from that of Ding, Li and Xin (2018). |
| title | A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.23946 |