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arXiv · 1706.07726

Ground state of the conformal flow on $\mathbb{S}^3$

Piotr Bizoń·Dominika Hunik-Kostyra·Dmitry Pelinovsky
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Abstract

We consider the conformal flow model derived by Bizo\'n, Craps, Evnin, Hunik, Luyten, and Maliborski [Commun. Math. Phys. 353 (2017) 1179-1199] as a normal form for the conformally invariant cubic wave equation on $\mathbb{S}^3$. 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.

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Piotr Bizoń, Dominika Hunik-Kostyra, Dmitry Pelinovsky. 2017-06-23. Ground state of the conformal flow on $\mathbb{S}^3$. https://arxiv.org/abs/1706.07726

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