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Ground State of the Conformal Flow on 𝕊 3
Author(s) -
Bizoń Piotr,
HunikKostyra Dominika,
Pelinovsky Dmitry E.
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21815
Subject(s) - conformal map , ground state , mathematics , invariant (physics) , degeneracy (biology) , flow (mathematics) , conformal symmetry , state (computer science) , stability (learning theory) , nonlinear system , mathematical physics , energy (signal processing) , mathematical analysis , pure mathematics , physics , quantum mechanics , geometry , algorithm , bioinformatics , statistics , machine learning , computer science , biology
We consider the conformal flow model derived in Bizoń et al. (2017) as a normal form for the conformally invariant cubic wave equation on 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.