Refined Liouville-Type Theorems for the Stationary Navier--Stokes Equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917360924884992 |
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| author | Cho, Youseung Yang, Minsuk |
| author_facet | Cho, Youseung Yang, Minsuk |
| contents | We study smooth solutions to the three-dimensional stationary Navier--Stokes equations and establish new Liouville-type theorems under refined decay assumptions. Building on the work of Cho et al., we introduce a refinement to previously known integrability criteria and analyze the associated averaged quantities. Our main result shows that if the $L^p$ growth rate of a solution remains bounded for some $3/2 < p < 3$, then the solution must be trivial. The proof combines averaged decay estimates, energy inequalities, and an iteration scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined Liouville-Type Theorems for the Stationary Navier--Stokes Equations Cho, Youseung Yang, Minsuk Analysis of PDEs We study smooth solutions to the three-dimensional stationary Navier--Stokes equations and establish new Liouville-type theorems under refined decay assumptions. Building on the work of Cho et al., we introduce a refinement to previously known integrability criteria and analyze the associated averaged quantities. Our main result shows that if the $L^p$ growth rate of a solution remains bounded for some $3/2 < p < 3$, then the solution must be trivial. The proof combines averaged decay estimates, energy inequalities, and an iteration scheme. |
| title | Refined Liouville-Type Theorems for the Stationary Navier--Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.23833 |