Lagrangian for Navier-Stokes equations of motion: SDPD approach
Biological Physics
2026-02-04 v1
Abstract
The conditions necessary and sufficient for the Smoothed Dissipative Particle Dynamics (SDPD) equations of motion to have a Lagrangian that can be used for deriving these equations of motion, the Helmholtz conditions, are obtained and analysed. They show that for a finite number of SDPD particles the conditions are not satisfied; hence, the SDPD equations of motion can not be obtained using the classical Euler-Lagrange equation approach. However, when the macroscopic limit is considered, that is when the number of particles tends to infinity, the conditions are satisfied, thus providing the conceptual possibility of obtaining the Navier-Stokes equations from the principle of least action.
Keywords
Cite
@article{arxiv.2602.03480,
title = {Lagrangian for Navier-Stokes equations of motion: SDPD approach},
author = {Tatyana Kornilova and Anna Shokhina and Timothy Nerukh and Dmitry Nerukh},
journal= {arXiv preprint arXiv:2602.03480},
year = {2026}
}