Spectral properties and linear stability of self-similar wave maps

Autor(en)

Roland Donninger, Peter Christian Aichelburg

Abstrakt

We study co--rotational wave maps from $(3+1)$--Minkowski space to the three--sphere $S^3$. It is known that there exists a countable family $\{f_n\}$ of self--similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well--posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from $f_n$ by letting $n \to \infty$.

Organisation(en)

Gravitationsphysik

Journal

Journal of Hyperbolic Differential Equations

Band

6

Seiten

359-370

Anzahl der Seiten

12

ISSN

0219-8916

DOI

https://doi.org/10.1142/S0219891609001812

Publikationsdatum

2009

Peer-reviewed

Ja

ÖFOS 2012

1010 Mathematik, 1030 Physik, Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/0f1c3203-2f51-4fe4-a914-414e33f4a643