A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909202193055744 |
|---|---|
| author | Bulut, Aynur Huynh, Khang Manh |
| author_facet | Bulut, Aynur Huynh, Khang Manh |
| contents | In this paper, we use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai [15] which was developed in the context of periodic boundary conditions on a flat background, and which is based on a maximum principle for Fourier coefficients.
The extension to general manifolds requires several new ideas, connected to the less favorable spectral localization properties in our setting. Our arguments make use of frequency projection operators, multilinear estimates that originated in the study of the non-linear Schrödinger equation, and ideas from microlocal analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_07259 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds Bulut, Aynur Huynh, Khang Manh Analysis of PDEs Mathematical Physics In this paper, we use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai [15] which was developed in the context of periodic boundary conditions on a flat background, and which is based on a maximum principle for Fourier coefficients. The extension to general manifolds requires several new ideas, connected to the less favorable spectral localization properties in our setting. Our arguments make use of frequency projection operators, multilinear estimates that originated in the study of the non-linear Schrödinger equation, and ideas from microlocal analysis. |
| title | A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2009.07259 |