Differential invariants and quotient of the Euler equations on a sphere

Abstract: We consider the Euler system on a sphere written in stereographic coordinates. Since the system is underdetermined we consider flow of a medium taking into account thermodynamic equations of state.

Lie algebras of symmetries of the Euler system are found and we give their classification depending on possible equations of state. Among these Lie algebras there is one that preserves any thermodynamic equation. Such symmetries and the corresponding rational differential invariants we call kinematic. The field of kinematic differential invariants is described: basis differential invariants as well as invariant derivations are found. Then we find relations (syzygies) between the second-order invariants, from which we find a quotient equation for the Euler system on a sphere.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

Geometry of differential equations seminar