English

Mode stability of self-similar wave maps without symmetry in higher dimensions

Analysis of PDEs 2026-04-16 v2 Mathematical Physics math.MP Spectral Theory

Abstract

We consider wave maps from (1+d)(1+d)-dimensional Minkowski space into the dd-sphere. For every d3d \geq 3, there exists an explicit self-similar solution that exhibits finite time blowup. This solution is corotational and its mode stability in the class of corotational functions is known. Recently, Weissenbacher, Koch, and the first author proved mode stability without symmetry assumptions in d=3d =3. In this paper we extend this result to all d4d \geq 4. On a technical level, this is the first successful implementation of the quasi-solution method where two additional parameters are present.

Keywords

Cite

@article{arxiv.2601.19515,
  title  = {Mode stability of self-similar wave maps without symmetry in higher dimensions},
  author = {Roland Donninger and Frederick Moscatelli},
  journal= {arXiv preprint arXiv:2601.19515},
  year   = {2026}
}

Comments

34 pages, suggestions by referee incorporated, will appear in Trans. Amer. Math. Soc