Abstract
The modified Korteweg-de Vries equation (mKdV) is a relevant model for vortex filaments in fluid dynamics, in particular to give account of the dynamics of spirals making a corner. This kind of phenomont corresponds to self-similar solutions of (mKdV), and their perturbation. In this talk, we will review some recent works with Simão Correia and Luis Vega on this topic, notably the local Cauchy theory in a critical space containing the self-similar solutions, and the construction of solutions blowing up as the sum of a self-similar solution and a prescribed Perturbation.
