Integrability in Fluid Dynamics

TL;DR

This paper demonstrates that certain fluid dynamics systems, including relativistic and interacting cases, exhibit integrability characterized by infinite conserved quantities, using Hamiltonian formalism and Clebsch parametrization.

Contribution

It establishes the integrability of 3+1D free and interacting fluid systems, extending to relativistic cases, and introduces new conserved quantities using Clebsch parametrization.

Findings

Free inviscid fluid dynamics is integrable with infinite conserved quantities.

Interaction introduces new series of conserved quantities.

Relativistic fluid systems are also shown to be integrable.

Abstract

3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density dependent) interaction present, distinct infinite serieses of conserved quantities in involution are discovered. Clebsch parametrization of the velocity field is used in the the latter analysis. Relativistic generalization of the free system is also shown to be integrable.