An Lp-theory for fractional stationary Navier-Stokes equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909202552717312 |
|---|---|
| author | Jarrín, Oscar Vergara-Hermosilla, Gastón |
| author_facet | Jarrín, Oscar Vergara-Hermosilla, Gastón |
| contents | We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$Δ$) $α$/2 in the diffusion term. In the framework of Lebesgue and Lorentz spaces, we find some natural sufficient conditions on the external force and on the parameter $α$ to prove the existence and in some cases nonexistence of solutions. Secondly, we obtain sharp pointwise decaying rates and asymptotic profiles of solutions, which strongly depend on $α$. Finally, we also prove the global regularity of solutions. As a bi-product, we obtain some uniqueness theorems so-called Liouville-type results. On the other hand, our regularity result yields a new regularity criterion for the classical ( i.e. with $α$ = 2) stationary Navier-Stokes equations. Contents |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Lp-theory for fractional stationary Navier-Stokes equations Jarrín, Oscar Vergara-Hermosilla, Gastón Analysis of PDEs We consider the stationary (time-independent) Navier-Stokes equations in the whole threedimensional space, under the action of a source term and with the fractional Laplacian operator (--$Δ$) $α$/2 in the diffusion term. In the framework of Lebesgue and Lorentz spaces, we find some natural sufficient conditions on the external force and on the parameter $α$ to prove the existence and in some cases nonexistence of solutions. Secondly, we obtain sharp pointwise decaying rates and asymptotic profiles of solutions, which strongly depend on $α$. Finally, we also prove the global regularity of solutions. As a bi-product, we obtain some uniqueness theorems so-called Liouville-type results. On the other hand, our regularity result yields a new regularity criterion for the classical ( i.e. with $α$ = 2) stationary Navier-Stokes equations. Contents |
| title | An Lp-theory for fractional stationary Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.11078 |