Resonant normal forms describe energy transfer mechanisms between modes trapped in the confining geometry. In the context of the conformal flow on three-sphere, we prove that the energy attains a global constrained maximum at a family of particular stationary solutions which we call the ground state family. Using this fact and spectral properties of the linearized flow (which are interesting on their own due to a supersymmetric structure) we prove nonlinear orbital stability of the ground state family. Next step is to analyze bifurcation of other stationary solutions in the conformal flow.
Impact
Impact of the project is in the fundamental research on resonant normal forms and wave turbulence models.
Student Experience
The project involves a PhD student from Jagiellonian University, Krakow.
