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arXiv · 0908.1201

A construction of blow up solutions for co-rotational wave maps

Catalin I. Carstea
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Abstract

The existence of co-rotational finite time blow up solutions to the wave map problem from R^{2+1} into N, where N is a surface of revolution with metric dρ^2+g(ρ)^2 dθ^2, g an entire function, is proven. These are of the form u(t,r)=Q(λ(t)t)+R(t,r), where Q is a time independent solution of the co-rotational wave map equation -u_{tt}+u_{rr}+r^{-1}u_r=r^{-2}g(u)g'(u), λ(t)=t^{-1-ν}, ν>1/2 is arbitrary, and R is a term whose local energy goes to zero as t goes to 0.

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Catalin I. Carstea. 2009-08-09. A construction of blow up solutions for co-rotational wave maps. https://doi.org/10.1007/s00220-010-1118-4

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