The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908942756478976 |
|---|---|
| author | Wang, Chao Yue, Jingchao Zhang, Zhifei |
| author_facet | Wang, Chao Yue, Jingchao Zhang, Zhifei |
| contents | This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the existence and uniqueness of solutions subject to the non-slip boundary condition. This result was established in \cite{Ken} under the condition that the total mass is sufficiently small. Here, we eliminate the smallness assumption by analyzing the linearized operator near the point vortex and constructing a tailored functional framework-one designed to capture the distinct behaviors of the solution in the vicinity of the point vortex and the boundary, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05765 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution Wang, Chao Yue, Jingchao Zhang, Zhifei Analysis of PDEs This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the existence and uniqueness of solutions subject to the non-slip boundary condition. This result was established in \cite{Ken} under the condition that the total mass is sufficiently small. Here, we eliminate the smallness assumption by analyzing the linearized operator near the point vortex and constructing a tailored functional framework-one designed to capture the distinct behaviors of the solution in the vicinity of the point vortex and the boundary, respectively. |
| title | The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.05765 |