A proof for the mode stability of a self-similar wave map. (4th July 2016)

• Record Type: Journal Article
• Authors: Costin, O; Donninger, R; Xia, X
• Is Part Of: Nonlinearity. Volume 29:Number 8(2016:Aug.)
• Page Start: 2451
• Page End: 2473
• Publication Date: 2016-07-04
• Subjects: wave maps -- self-similar solution -- nonself-adjoint spectral theory; 35L70 -- 35B44 -- 35B35; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/8/2451
• Languages: English
• ISSNs: 0951-7715

Abstract

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.