首页> 外文期刊>Journal of the European Mathematical Society: JEMS >Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
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Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation

机译:能量临界波动方程的小径向II型爆破解的爆破分布图的普遍性

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Consider the energy-critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, under an appropriate smallness assumption, any type II blow-up radial solution is essentially the sum of a rescaled W concentrating at the origin and a small remainder which is continuous with respect to the time variable in the energy space. This is coherent with the solutions constructed by Krieger, Schlag and Tataru. One ingredient of our proof is that the unique radial solution which is compact up to scaling is equal to W up to symmetries.
机译:考虑欧几里得空间上的能量临界聚焦波方程。该方程的Ⅱ型爆破解是一种存在时间有限但仍在能量空间内的解。这项工作的目的是展示此类解决方案的通用属性。令W为方程的唯一径向正固定解。我们的主要结果是,在第3维中,在适当的小假设的前提下,任何II型爆炸径向解本质上都是重新定标的W集中在原点的总和与相对于时间变量连续的小余数之和。能量空间。这与Krieger,Schlag和Tataru构建的解决方案保持一致。我们证明的一个要素是,在按比例压缩之前,唯一的径向解等于在对称时等于W。

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