Mode stability of self-similar wave maps in higher dimensions

Abstract

We consider co-rotational wave maps from Minkowski space in $d+1$ dimensions to the $d$-sphere. Recently, Bizoń and Biernat found explicit self-similar solutions for each dimension $d\ge 4$. We give a rigorous proof for the mode stability of these self-similar wave maps.

arXiv comment16 pages; v2 second reference to [4] removed, implicit claim in case k=2 now stated as a lemma; v3 section 5 added, references updated, to appear in Comm. Math. Phys

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• On the existence and stability of blowup for wave maps into a negatively curved target
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