Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910614387949568 |
|---|---|
| author | Abbatiello, Anna Basaric, Danica Chaudhuri, Nilasis Feireisl, Eduard |
| author_facet | Abbatiello, Anna Basaric, Danica Chaudhuri, Nilasis Feireisl, Eduard |
| contents | We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain:
Blow up criteria for strong solutions,
Local existence of strong solutions in the optimal L^p-L^q framework,
Alternative proof of the existing results on local well posedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions Abbatiello, Anna Basaric, Danica Chaudhuri, Nilasis Feireisl, Eduard Analysis of PDEs Mathematical Physics We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain: Blow up criteria for strong solutions, Local existence of strong solutions in the optimal L^p-L^q framework, Alternative proof of the existing results on local well posedness. |
| title | Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2409.13459 |