Infoscience

Thesis

# Optimal polynomial blow up range for critical wave maps

We prove that the critical Wave Maps equation with target $S^2$ and origin ℝ$^{2+1}$ admits energy class blow up solutions of the form $u(t, r) = Q(\lambda(t)r) + \epsilon(t, r)$ where $Q:ℝ²\rightarrow S^2$ is the ground state harmonic map and $\lambda(t) = t^{-1-\nu}$ for any $\nu>0$. This extends the work, where such solutions were constructed under the assumption $\nu>\frac{1}{2}$. Also in the later chapter, we give the necessary remarks and key changes one needs to notice while the same problem is considered in a more general case while $\cal{N}$ is a surface of revolution. We are also able to extends the blow-up range in Carstea's work to $\nu>0$. In light of a result of Struwe, our results are optimal for polynomial blow up rates.

Thèse École polytechnique fédérale de Lausanne EPFL, n° 6432 (2015)
Programme doctoral Mathématiques
Faculté des sciences de base
Institut de mathématiques d'analyse et applications
Chaire des équations différentielles partielles
Jury: Prof. M. Troyanov (président) ; Prof. J. Krieger (directeur) ; Prof. G. Crippa, Prof. G. Holzegel, Prof. D. Kressner (rapporteurs)

Public defense: 2015-1-8

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Record created on 2014-12-22, modified on 2016-08-09