The present work deals with two important theoretical aspects of the 2D fluid theory for non‐neutral plasmas: the study of the merger between plasma vortices and the non‐linear study of the evolution of the diocotron instability. In both cases, analytical and semi‐analytical models have been deduced and the results have been tested by means of a numerical code based on the contour dynamics technique developed by the Authors. © 2003 American Institute of Physics