# Concentration Compactness for Critical Radial Wave Maps

@article{Chiodaroli2016ConcentrationCF, title={Concentration Compactness for Critical Radial Wave Maps}, author={Elisabetta Chiodaroli and Joachim Krieger and Jonas L{\"u}hrmann}, journal={Annals of PDE}, year={2016}, volume={4}, pages={1-148} }

We consider radially symmetric, energy critical wave maps from $$(1+2)$$(1+2)-dimensional Minkowski space into the unit sphere $$\mathbb {S}^m$$Sm, $$m \ge 1$$m≥1, and prove global regularity and scattering for classical smooth data of finite energy. In addition, we establish a priori bounds on a suitable scattering norm of the radial wave maps and exhibit concentration compactness properties of sequences of radial wave maps with uniformly bounded energies. This extends and complements the… Expand

#### 4 Citations

Non-Uniqueness of Bubbling for Wave Maps

- Mathematics, Physics
- 2020

We consider wave maps from $\mathbb R^{2+1}$ to a $C^\infty$-smooth Riemannian manifold, $\mathcal N$. Such maps can exhibit energy concentration, and at points of concentration, it is known that the… Expand

Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case.

- Mathematics, Physics
- 2017

In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation in the subcritical perturbation class. This result may… Expand

Asymptotic stability of small energy harmonic maps under the wave map on 2D hyperbolic space

- Mathematics
- 2017

In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map. This result may be seen as an example supporting the soliton… Expand

Asymptotic stability of large energy harmonic maps under the wave map from 2D hyperbolic spaces to 2D hyperbolic spaces

- Mathematics
- 2017

In this paper, we prove that the large energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation.

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