Topological Features of Inviscid Flows

Abstract

The Euler equations for an incompressible inviscid fluid in dimension three possess a wealth of topological phenomena woven into the dynamical and geometric properties of the fluid. Focusing first on steady Euler fields, we outline known results, giving special attention to the Beltrami fields and the contemporary topological techniques required to elucidate their dynamical features. We also propose a topological perspective for understanding the global dynamics of the Euler equations on the space of velocity fields.