Stable blowup for supercritical wave maps into perturbed spheres

2025/03/06 by Donninger, Roland, Schörkhuber, Birgit, Wittenstein, Alexander
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.04425

Abstract

We consider wave maps from (1+d)-dimensional Minkowski space, d≥3, into rotationally symmetric manifolds which arise from small perturbations of the sphere \mathbb S^d. We prove the existence of co-rotational self-similar finite time blowup solutions with smooth blowup profiles. Furthermore, we show the nonlinear asymptotic stability of these solutions under suitably small co-rotational perturbations on the full space.

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