Inverse problem in the calculus of variations -- functional and antiexact forms
Mathematical Physics
2022-09-22 v3 Analysis of PDEs
Differential Geometry
math.MP
Abstract
We connect the well-known theory of functional forms of variational bicomplex with the theory of antiexact differential forms. We identify antiexact functional forms as an obstruction to the variationality of differential equations. The most prominent result of this observation is the formulation of the variational problem for some differential equations that are not variational and neither have a variational multiplier. Heat, Navier-Stokes, and KdV equations illustrate this new variational principle.
Cite
@article{arxiv.2110.04346,
title = {Inverse problem in the calculus of variations -- functional and antiexact forms},
author = {Radosław Antoni Kycia},
journal= {arXiv preprint arXiv:2110.04346},
year = {2022}
}
Comments
16 pages