Variational Dual Solutions for Incompressible Fluids
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908816883318784 |
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| author | Acharya, Amit Stroffolini, Bianca Zarnescu, Arghir |
| author_facet | Acharya, Amit Stroffolini, Bianca Zarnescu, Arghir |
| contents | We consider a construction proposed in \cite{acharyaQAM} that builds on the notion of weak solutions for incompressible fluids to provide a scheme that generates variationally a certain type of dual solutions. If these dual solutions are regular enough one can use them to recover standard solutions. The scheme provides a generalisation of a construction of Y$.$Brenier for the Euler equations. We rigorously analyze the scheme, extending the work of Y$.$Brenier for Euler, and also provide an extension of it to the case of the Navier-Stokes equations. Furthermore we obtain the inviscid limit of Navier-Stokes to Euler as a $Γ$-limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Dual Solutions for Incompressible Fluids Acharya, Amit Stroffolini, Bianca Zarnescu, Arghir Analysis of PDEs We consider a construction proposed in \cite{acharyaQAM} that builds on the notion of weak solutions for incompressible fluids to provide a scheme that generates variationally a certain type of dual solutions. If these dual solutions are regular enough one can use them to recover standard solutions. The scheme provides a generalisation of a construction of Y$.$Brenier for the Euler equations. We rigorously analyze the scheme, extending the work of Y$.$Brenier for Euler, and also provide an extension of it to the case of the Navier-Stokes equations. Furthermore we obtain the inviscid limit of Navier-Stokes to Euler as a $Γ$-limit. |
| title | Variational Dual Solutions for Incompressible Fluids |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.04911 |