A Proof for the Mode Stability of a Self-similar Wave Map
Ovidiu Costin, Roland Donninger, Xiaoyue Xia
TL;DR
This paper provides a rigorous proof of the mode stability of a fundamental self-similar wave map solution in the SU(2) sigma model, advancing the understanding of its nonlinear stability.
Contribution
It offers the final rigorous proof of mode stability for the Shatah-Turok-Spergel wave map, completing the analysis of its nonlinear stability.
Findings
Proof of mode stability for the self-similar wave map
Supports the nonlinear stability of the wave map
Builds on previous results to finalize stability analysis
Abstract
We study the fundamental self-similar solution to the SU(2) sigma model, found by Shatah and Turok-Spergel. We give a rigorous proof for its mode stability. Based on earlier results by the second author, the present paper constitutes the last building block for a completely rigorous proof of the nonlinear stability of the Shatah-Turok-Spergel wave map.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems