The Navier-Stokes equations with transport noise in critical $H^{1/2}$ space
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912690353471488 |
|---|---|
| author | Aydın, Mustafa Sencer Xu, Fanhui |
| author_facet | Aydın, Mustafa Sencer Xu, Fanhui |
| contents | We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to $H^{1/2}$ almost surely, we establish the existence and uniqueness of a local-in-time probabilistically strong solution. Moreover, we show that the probability of global existence can be made arbitrarily close to $1$ by choosing the initial data norm sufficiently small, and that the solution norm remains small for all time. Our analysis is independent of the compactness of the spatial domain, and consequently, the results apply both to the three-dimensional torus and to the whole space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Navier-Stokes equations with transport noise in critical $H^{1/2}$ space Aydın, Mustafa Sencer Xu, Fanhui Probability Analysis of PDEs We study the Navier-Stokes equations with transport noise in critical function spaces. Assuming the initial data belongs to $H^{1/2}$ almost surely, we establish the existence and uniqueness of a local-in-time probabilistically strong solution. Moreover, we show that the probability of global existence can be made arbitrarily close to $1$ by choosing the initial data norm sufficiently small, and that the solution norm remains small for all time. Our analysis is independent of the compactness of the spatial domain, and consequently, the results apply both to the three-dimensional torus and to the whole space. |
| title | The Navier-Stokes equations with transport noise in critical $H^{1/2}$ space |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2511.04138 |