The existence of co-rotational finite time blow up solutions to the wave map problem from , where N is a surface of revolution with metric d ρ 2 + g(ρ)2 dθ2, g an entire function, is proven. These are of the form , 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 is a term whose local energy goes to zero as t → 0.
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机译：来自的波动图问题的同旋转有限时间爆破解的存在，其中N是度量dρ 2 + g（ρ） 2 的旋转表面证明了dθ 2 的全部功能。这些形式为，其中Q是同旋转波图方程-u tt + u rr + r -1的与时间无关的解 u r = r −2 g（u）g′（u），λ（t）= t −1-ν ， ν> 1/2是任意的，并且是当t→0时局部能量变为零的项。
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