On uniqueness for hyperbolic half-wave maps in dimension d ≥ 3

2024/07/08 by Silvino Reyes Farina, Farina, Silvino Reyes
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.06448

Abstract

Half-wave maps appear in the physics literature as the continuum limit of Calogero-Moser spin systems. We obtain a uniqueness result for the Half-Wave Maps equation in dimension d ≥ 3 in the natural energy class with ℍ² target. In the proof, we differentiate in time to arrive at a wave-type equation and isometrically embed ℍ² into some ℝ^m using the Nash embedding theorem. Relying on geometric properties of ℍ², combined with fractional Leibniz rules and commutator estimates, we then use a Grönwall inequality argument to obtain uniqueness.

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