Global smooth solutions by transport noise of 3D Navier-Stokes equations with small hyperviscosity
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912054795829248 |
|---|---|
| author | Agresti, Antonio |
| author_facet | Agresti, Antonio |
| contents | The existence of global smooth solutions to the Navier-Stokes equations (NSEs) with hyperviscosity $(-Δ)^γ$ is open unless $γ$ is close to the J.-L. Lions exponent $ \frac{5}{4}$ at which the energy balance is strong enough to prevent singularity formation. If $1<γ\ll \frac{5}{4}$, then the global well-posedness of the hyperviscous NSEs is widely open as for the usual NSEs. In this paper, for all $γ>1$, we show the existence of a transport noise for which global smooth solutions to the stochastic hyperviscous NSEs on the three-dimensional torus exist with high probability. In particular, a suitable transport noise considerably improves the known well-posedness results in the deterministic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global smooth solutions by transport noise of 3D Navier-Stokes equations with small hyperviscosity Agresti, Antonio Analysis of PDEs Probability Primary: 60H50, Secondary: 60H15, 76M35, 35Q35 The existence of global smooth solutions to the Navier-Stokes equations (NSEs) with hyperviscosity $(-Δ)^γ$ is open unless $γ$ is close to the J.-L. Lions exponent $ \frac{5}{4}$ at which the energy balance is strong enough to prevent singularity formation. If $1<γ\ll \frac{5}{4}$, then the global well-posedness of the hyperviscous NSEs is widely open as for the usual NSEs. In this paper, for all $γ>1$, we show the existence of a transport noise for which global smooth solutions to the stochastic hyperviscous NSEs on the three-dimensional torus exist with high probability. In particular, a suitable transport noise considerably improves the known well-posedness results in the deterministic setting. |
| title | Global smooth solutions by transport noise of 3D Navier-Stokes equations with small hyperviscosity |
| topic | Analysis of PDEs Probability Primary: 60H50, Secondary: 60H15, 76M35, 35Q35 |
| url | https://arxiv.org/abs/2406.09267 |