Spectral properties and linear stability of self-similar wave maps
- Author(s)
- Roland Donninger, Peter Christian Aichelburg
- Abstract
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(s)
- Gravitational Physics
- Journal
- Journal of Hyperbolic Differential Equations
- Volume
- 6
- Pages
- 359-370
- No. of pages
- 12
- ISSN
- 0219-8916
- DOI
- https://doi.org/10.1142/S0219891609001812
- Publication date
- 2009
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 1010 Mathematics, 1030 Physics, Astronomy
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/spectral-properties-and-linear-stability-of-selfsimilar-wave-maps(0f1c3203-2f51-4fe4-a914-414e33f4a643).html