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arXiv · 2409.04911

Variational Dual Solutions for Incompressible Fluids

Amit Acharya·Bianca Stroffolini·Arghir Zarnescu
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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 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.

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Amit Acharya, Bianca Stroffolini, Arghir Zarnescu. 2026-02-05. Variational Dual Solutions for Incompressible Fluids. https://arxiv.org/abs/2409.04911

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