Ground State of the Conformal Flow on 𝕊3

Abstract We consider the conformal flow model derived in Bizoń et al. (2017) as a normal form for the conformally invariant cubic wave equation on 𝕊 3 . We prove that the energy attains a global constrained maximum at a family of particular stationary solutions that we call the ground state family. Using this fact and spectral properties of the linearized flow (which are interesting in their own right 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. © 2019 Wiley Periodicals, Inc.