Renormalization and blow up for charge one equivariant critical wave maps
Analysis of PDEs
2015-06-26 v1 Mathematical Physics
math.MP
Abstract
We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis.
Cite
@article{arxiv.math/0610248,
title = {Renormalization and blow up for charge one equivariant critical wave maps},
author = {Joachim Krieger and Wilhelm Schlag and Daniel Tataru},
journal= {arXiv preprint arXiv:math/0610248},
year = {2015}
}