Dissipative Vortex Dynamics and Magnus Force

Abstract

A single vortexin the infinite plane, emerging as a solution of a conservative PDE with global U(1) and Galilean symmetry, is a very special object. Its singular properties, as well as special symmetries of the governing equation, which are broken in more realistic models, have been a source of paradoxes and erroneous conclusions during the long history of theory of vortex motion. A detailed review containing further references is found in the recent monograph by this author [1]. This communication sketches main ideas and pitfalls of singular perturbation techniques that allow to describe slow vortex motion including effects of weak dissipation.