Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915987081658368 |
|---|---|
| author | Vergara-Hermosilla, Gaston |
| author_facet | Vergara-Hermosilla, Gaston |
| contents | We study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the velocity, namely $u_ρ(x) \in L^p(\mathbb{R}^3)$ with $3/2 < p \leq 3$. We also establish a uniqueness result in a variable-exponent setting, where an $L^6$-type condition is required only on a bounded region, while the exponent approaches the critical value $3$ at infinity. Our analysis reveals that the rigidity of the stationary Navier--Stokes system can be driven by localized and radial integrability properties, rather than uniform global conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component Vergara-Hermosilla, Gaston Analysis of PDEs 35Q30 We study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the velocity, namely $u_ρ(x) \in L^p(\mathbb{R}^3)$ with $3/2 < p \leq 3$. We also establish a uniqueness result in a variable-exponent setting, where an $L^6$-type condition is required only on a bounded region, while the exponent approaches the critical value $3$ at infinity. Our analysis reveals that the rigidity of the stationary Navier--Stokes system can be driven by localized and radial integrability properties, rather than uniform global conditions. |
| title | Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component |
| topic | Analysis of PDEs 35Q30 |
| url | https://arxiv.org/abs/2605.05647 |