Helicity in dispersive fluid mechanics
Analysis of PDEs
2024-04-01 v1
Abstract
By dispersive models of fluid mechanics we are referring to the Euler-Lagrange equations for the constrained Hamilton action functional where the internal energy depends on high order derivatives of unknowns. The mass conservation law is considered as a constraint. The corresponding Euler-Lagrange equations include, in particular, the van der Waals--Korteweg model of capillary fluids, the model of fluids containing small gas bubbles and the model describing long free-surface gravity waves. We obtain new conservation laws generalizing the helicity conservation for classical barotropic fluids.
Cite
@article{arxiv.2403.20072,
title = {Helicity in dispersive fluid mechanics},
author = {S. L. Gavrilyuk and H. Gouin},
journal= {arXiv preprint arXiv:2403.20072},
year = {2024}
}