Variational Dual Solutions for Incompressible Fluids

Fuente: arXiv
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Autores principales: Acharya, Amit, Stroffolini, Bianca, Zarnescu, Arghir
Formato: Preprint
Publicado: 2024
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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