Stability of Spherically Symmetric Wave Maps

@inproceedings{Krieger2006StabilityOS,
  title={Stability of Spherically Symmetric Wave Maps},
  author={Joachim Krieger},
  year={2006}
}
We study Wave Maps from R2+1 to the hyperbolic plane H2 with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some H1+μ, μ > 0. We show that such Wave Maps don’t develop singularities in finite time and stay close to the Wave Map extending the spherically symmetric data(whose existence is ensured by a theorem of Christodoulou-Tahvildar-Zadeh) with respect to all H1+δ , δ < μ0 for suitable μ0(μ) > 0. We obtain a similar result… CONTINUE READING