Sharp Asymptotic Behavior of the Steady Pressure-free Prandtl system
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916729328762880 |
|---|---|
| author | Gao, Chen Zhao, Chuankai |
| author_facet | Gao, Chen Zhao, Chuankai |
| contents | This paper investigates the asymptotic behavior of solutions to the steady pressure-free Prandtl system. By employing a modified von Mises transformation, we rigorously prove the far-field convergence of Prandtl solutions to Blasius flow. A weighted energy method is employed to establish the optimal convergence rate assuming that the initial data constitutes a perturbation of the Blasius profile. Furthermore, a sharp maximum principle technique is applied to derive the optimal convergence rate for concave initial data. The critical weights and comparison functions depend on the first eigenfunction of the linearized operator associated with the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11870 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Asymptotic Behavior of the Steady Pressure-free Prandtl system Gao, Chen Zhao, Chuankai Analysis of PDEs This paper investigates the asymptotic behavior of solutions to the steady pressure-free Prandtl system. By employing a modified von Mises transformation, we rigorously prove the far-field convergence of Prandtl solutions to Blasius flow. A weighted energy method is employed to establish the optimal convergence rate assuming that the initial data constitutes a perturbation of the Blasius profile. Furthermore, a sharp maximum principle technique is applied to derive the optimal convergence rate for concave initial data. The critical weights and comparison functions depend on the first eigenfunction of the linearized operator associated with the system. |
| title | Sharp Asymptotic Behavior of the Steady Pressure-free Prandtl system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.11870 |