Publication 24-CNA-010

Variational Dual Solutions for Incompressible Fluids

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Bianca Stroffolini
Dipartimento di Matematica e Applicazioni
Università di Napoli "Federico II"
Napoli, Italy
bstroffo@unina.it

Arghir Zarnescu
BCAM, Basque Center for Applied Mathematics Mazarredo
Bizkaia, Spain
IKERBASQUE, Basque Foundation for Science
Bizkaia, Spain
"Simion Stoilow" Institute of the Romanian Academy
Bucharest, Romania
azarnescu@bcamath.org

Abstract: We consider a construction proposed in [Ach22] 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 $\Gamma$-limit.

Get the paper in its entirety as  24-CNA-010.pdf

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