P. Bizon, D. Hunik-Kostyra, and D.E. Pelinovsky

Ground state of the conformal flow on S3


Abstract:
We consider the conformal flow model derived as a normal form for the conformally invariant cubic wave equation on S3. 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. The main difficulty in the proof is due to the degeneracy of the ground state family as a constrained maximizer of the energy.

Keywords:
Conformal flow, resonant normal form, ground state, constrained maximization, spectral stability, nonlinear stability.