Variational Dual Solutions for Incompressible Fluids
Analysis of PDEs
2026-02-09 v3
Abstract
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 YBrenier for the Euler equations. We rigorously analyze the scheme, extending the work of YBrenier 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 -limit.
Cite
@article{arxiv.2409.04911,
title = {Variational Dual Solutions for Incompressible Fluids},
author = {Amit Acharya and Bianca Stroffolini and Arghir Zarnescu},
journal= {arXiv preprint arXiv:2409.04911},
year = {2026}
}