Threshold for blowup for equivariant wave maps in higher dimensions. (7th March 2017)

• Record Type: Journal Article
• Authors: Biernat, Paweł; Bizoń, Piotr; Maliborski, Maciej
• Is Part Of: Nonlinearity. Volume 28:Number 4(2015:Apr.)
• Page Start: 1513
• Page End: 1522
• Publication Date: 2017-03-07
• Subjects: wave maps -- self-similar blowup -- critical behavior; 35L70; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa61ab
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider equivariant wave maps from R d + 1 to S d in supercritical dimensions 3 ⩽ d ⩽ 6 . Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability. To probe self-similar blowup, we develop a novel numerical method, based on an adaptive rescaling of coordinates, which may be of independent interest in numerical studies of singularity formation.