The well-posedness of three-dimensional Navier-Stokes and magnetohydrodynamic equations with partial fractional dissipation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915686978158592 |
|---|---|
| author | Ma, Qibo Li, Li |
| author_facet | Ma, Qibo Li, Li |
| contents | It is well-known that if one replaces standard velocity and magnetic dissipation by $(-Δ)^αu$ and $(-Δ)^βb$ respectively, the magnetohydrodynamic equations are well-posed for $α\ge\frac{5}{4}$ and $α+ β\ge \frac{5}{2}$. This paper considers the 3D Navier-Stokes and magnetohydrodynamic equations with partial fractional hyper-dissipation. It is proved that when each component of the velocity and magnetic field lacks dissipation along some direction, the existence and conditional uniqueness of the solution still hold. This paper extends the previous results in (Yang, Jiu and Wu J. Differential Equations 266(1): 630-652, 2019) to a more general case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The well-posedness of three-dimensional Navier-Stokes and magnetohydrodynamic equations with partial fractional dissipation Ma, Qibo Li, Li Analysis of PDEs It is well-known that if one replaces standard velocity and magnetic dissipation by $(-Δ)^αu$ and $(-Δ)^βb$ respectively, the magnetohydrodynamic equations are well-posed for $α\ge\frac{5}{4}$ and $α+ β\ge \frac{5}{2}$. This paper considers the 3D Navier-Stokes and magnetohydrodynamic equations with partial fractional hyper-dissipation. It is proved that when each component of the velocity and magnetic field lacks dissipation along some direction, the existence and conditional uniqueness of the solution still hold. This paper extends the previous results in (Yang, Jiu and Wu J. Differential Equations 266(1): 630-652, 2019) to a more general case. |
| title | The well-posedness of three-dimensional Navier-Stokes and magnetohydrodynamic equations with partial fractional dissipation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.06489 |