Variational principles for nonlinear PDE systems via duality

2021/08/19 by Amit Acharya, Acharya, Amit · 2 citations
Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2108.08902

openalex publication_date 2021/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Discretization and convergence of the ballistic Benamou-Brenier formulation of the porous medium and Burgers equations
• Dual Variational Principles for Curl Forces

Related

• On a general variational framework for existence and uniqueness in Differential Equations
• Variational Dual Solutions for Incompressible Fluids
• Existence of a Variational Principle for PDEs with Symmetries and Current Conservation
• Variational Principle for Velocity-Pressure Formulation of Navier-Stokes\n Equations
• Variational resolution for some general classes of nonlinear evolutions. Part I