Bibliographic Details
| Title: |
Quasi-periodic solutions for the incompressible Navier-Stokes equations with nonlocal diffusion |
| Authors: |
Shuguan Ji, Yanshuo Li |
| Source: |
Electronic Research Archive, Vol 31, Iss 12, Pp 7182-7194 (2023) |
| Publisher Information: |
AIMS Press, 2023. |
| Publication Year: |
2023 |
| Collection: |
LCC:Mathematics
LCC:Applied mathematics. Quantitative methods |
| Subject Terms: |
navier-stokes (ns) equations, nonlocal diffusion, quasi-periodic solutions, asymptotic stability, exponential decay, Mathematics, QA1-939, Applied mathematics. Quantitative methods, T57-57.97 |
| More Details: |
This paper studied the incompressible Navier-Stokes (NS) equations with nonlocal diffusion on $ \mathbb{T}^d (d \ge 2) $. Driven by a time quasi-periodic force, the existence of time quasi-periodic solutions in the Sobolev space was established. The proof was based on the decomposition of the unknowns into the spatial average part and spatial oscillating one. The former were sought under the Diophantine non-resonance assumption, and the latter by the contraction mapping principle. Moreover, by constructing suitable time weighted function space and using the Banach fixed point theorem, the asymptotic stability of quasi-periodic solutions and the exponential decay of perturbation were proved. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2688-1594 |
| Relation: |
https://doaj.org/toc/2688-1594 |
| DOI: |
10.3934/era.2023363?viewType=HTML |
| DOI: |
10.3934/era.2023363 |
| Access URL: |
https://doaj.org/article/ec52e561ac1c43a79fe17701ebca8b1b |
| Accession Number: |
edsdoj.52e561ac1c43a79fe17701ebca8b1b |
| Database: |
Directory of Open Access Journals |
