Renormalization and blow up for charge one equivariant critical wave maps期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Renormalization and blow up for charge one equivariant critical wave maps

Authors:	J Krieger W Schlag D Tataru

Institution:	(1) Dept. of Mathematics, Science Center, Harvard University, Cambridge, MA 1 Oxford Street, 02138, USA;(2) Department of Mathematics, The University of Chicago, Chicago, IL 5734 South University Avenue, 60637, USA;(3) Department of Mathematics, The University of California at Berkeley, Berkeley, CA Evans Hall, 94720, USA

Abstract:	We prove the existence of equivariant finite time blow-up solutions for the wave map problem from ℝ²⁺¹→S ² of the form $u(t,r)=Q(\lambda(t)r)+\mathcal{R}(t,r)$ where u is the polar angle on the sphere, $Q(r)=2\arctan r$ is the ground state harmonic map, λ(t)=t ^-1-ν, and $\mathcal{R}(t,r)$ is a radiative error with local energy going to zero as t→0. The number $\nu>\frac{1}{2}$ can be prescribed arbitrarily. This is accomplished by first “renormalizing” the blow-up profile, followed by a perturbative analysis. Mathematics Subject Classification (1991) 35L05, 35Q75, 35P25

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