Research

RESEARCH INTERESTS

My focus is on the use of Normal Forms techniques to study the motion of fluids, like the existence of invariant structures and the long time evolution of initial data. The solidity and the flexibility of this approach has been proved to be strong, with several different applications. In my works, I achieved positive results in this direction for the Water Waves equations [5,7,8], for the Euler and Navier-Stokes equations [2,3,4] and for rotating fluids [1]. In most of these works, an important side result that it is obtained by our methods is the stability of the solutions under small perturbations. Thanks also for the rigorous methodology, these works received a favorable reception both at the editorial level and by the community at various conferences. Future and current perspectives include the analysis of pairs of vortex patches and the creation of instabilities around constant velocity fields for the Euler equations.