Spectral Properties and Linear Stability of Self-Similar Wave Maps

Details Spectral Properties and Linear Stability of Self-Similar Wave Maps Spectral Properties and Linear Stability of Self-Similar Wave Maps

2007-10-19

arxiv.org/abs/0710.3703v3

J. Hyperbolic Differ. Equ. 6 (2009), no. 2, pp. 359--370

Physics

Mathematical Physics

Some extensions added to match the published version

Scientific paper

10.1142/S0219891609001812

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 $n \to \infty$.

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