A Proof for the Mode Stability of a Self-similar Wave Map

2014/11/11 by Costin, Ovidiu, Donninger, Roland, Xia, Xiaoyue · 1 citation
#35B35 #35B44 #35C05 #35L05 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1411.2947

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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