eBook ISBN:  9781470404574 
Product Code:  MEMO/181/853.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 
eBook ISBN:  9781470404574 
Product Code:  MEMO/181/853.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 181; 2006; 80 ppMSC: Primary 35
We study Wave Maps from \({\mathbf{R}}^{2+1}\) to the hyperbolic plane \({\mathbf{H}}^{2}\) with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some \(H^{1+\mu}\), \(\mu>0\). 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 ChristodoulouTahvildarZadeh) with respect to all \(H^{1+\delta}, \delta < \mu_{0}\) for suitable \(\mu_{0}(\mu)>0\). We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This strengthens a theorem of Sideris for this context.

Table of Contents

Chapters

1. Introduction, controlling spherically symmetric wave maps

2. Technical preliminaries. Proofs of main theorems

3. The proof of Proposition 2.2

4. Proof of Theorem 2.3


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We study Wave Maps from \({\mathbf{R}}^{2+1}\) to the hyperbolic plane \({\mathbf{H}}^{2}\) with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some \(H^{1+\mu}\), \(\mu>0\). 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 ChristodoulouTahvildarZadeh) with respect to all \(H^{1+\delta}, \delta < \mu_{0}\) for suitable \(\mu_{0}(\mu)>0\). We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This strengthens a theorem of Sideris for this context.

Chapters

1. Introduction, controlling spherically symmetric wave maps

2. Technical preliminaries. Proofs of main theorems

3. The proof of Proposition 2.2

4. Proof of Theorem 2.3