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Stable blowup for supercritical wave maps into perturbed spheres

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arxiv 2503.04425 v1 pith:5VOLFWHR submitted 2025-03-06 math.AP math.CAmath.FA

Roland Donninger , Birgit Schörkhuber , Alexander Wittenstein This is my paper · ORCID
classification math.APmath.CAmath.FA
keywords blowupco-rotationalmapsperturbationssmallsolutionsspacewave
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abstract

We consider wave maps from $(1+d)$-dimensional Minkowski space, $d\geq3$, 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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  1. Stable blowup for the harmonic map heat flow into perturbed spheres

    math.AP 2026-08 conditional novelty 7.0 of 10

    Small smooth deformations of the sphere still admit stable self-similar blowup solutions for the corotational harmonic map heat flow in dimensions 3 to 6.

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