Variational principles for nonlinear PDE systems via duality

TL;DR

This paper introduces a formal method to derive variational principles for nonlinear PDE systems, demonstrated on Navier-Stokes, conservation laws, and Hamilton-Jacobi equations, enhancing analytical tools for these complex systems.

Contribution

It presents a novel formal methodology for constructing variational principles for nonlinear PDEs, applicable to various important systems.

Findings

Developed a systematic scheme for variational principles

Applied method to Navier-Stokes and conservation laws

Extended approach to Hamilton-Jacobi systems

Abstract

A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order conservation laws, and systems of Hamilton- Jacobi equations.