Kolmogorov $4/5$ law for the forced 3D Navier-Stokes equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912500240351232 |
|---|---|
| author | Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan |
| author_facet | Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan |
| contents | We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an $L^p$-in-time version of the Kolmogorov 4/5 law for the behavior of the averaged third order longitudinal structure function along the vanishing viscosity limit. The result has a natural probabilistic interpretation: the predicted behavior is observed on average after waiting for some sufficiently generic random time. The sufficient condition is satisfied e.g. by the solutions constructed by Bruè, Colombo, Crippa, De~Lellis, and Sorella. In this particular case, our results can be applied to derive a bound for the exponent of the third order absolute structure function in accordance with the Kolmogorov turbulence theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kolmogorov $4/5$ law for the forced 3D Navier-Stokes equations Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan Analysis of PDEs We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an $L^p$-in-time version of the Kolmogorov 4/5 law for the behavior of the averaged third order longitudinal structure function along the vanishing viscosity limit. The result has a natural probabilistic interpretation: the predicted behavior is observed on average after waiting for some sufficiently generic random time. The sufficient condition is satisfied e.g. by the solutions constructed by Bruè, Colombo, Crippa, De~Lellis, and Sorella. In this particular case, our results can be applied to derive a bound for the exponent of the third order absolute structure function in accordance with the Kolmogorov turbulence theory. |
| title | Kolmogorov $4/5$ law for the forced 3D Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.14470 |