On the interplay between vortices and harmonic flows: Hodge decomposition of Euler's equations in 2d

Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller

Let $\Sigma$ be a compact manifold without boundary whose first homology is nontrivial. Hodge decomposition of the incompressible Euler's equation in terms of 1-forms yields a coupled P…