The modified Korteweg-de Vries equation (mKdV) is an asymptotic model for fluid dynamics, and its self-similar solutions are connected to the formation of spirals and corners in a vortex patch.
In this talk, I will present some joint works with Simão Correia (Lisbon) and Luis Vega (Bilbao) regarding stability and perturbation of the blowup dynamic of self-similar solutions of (mKdV).