Bounds on the speed of type II blow-up for the energy critical wave equation in the radial case
Bounds on the speed of type II blow-up for the energy critical wave equation in the radial case
复制标题
径向情况下能量临界波动方程II型爆炸速度的界限
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Jacek Jendrej
中科院分区：
文献类型：
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作者：
Jacek Jendrej
我们考虑了空间维Nin {3，4，5}$中径向数据的聚焦能量临界波动方程。我们研究II型爆破解决方案，集中一个泡沫的能量。已知这样的解在能量空间中分解为气泡和渐近分布的总和。我们证明的情况下，当渐近轮廓是充分经常的爆破速度的界限。这些界限在维数N = 5时是最优的。我们还证明了，如果渐近轮廓是充分经常的，那么它不能严格负的原点。
We consider the focusing energy-critical wave equation in space dimension $Nin {3, 4, 5}$ for radial data. We study type II blow-up solutions which concentrate one bubble of energy. It is known that such solutions decompose in the energy space as a sum of the bubble and an asymptotic profile. We prove bounds on the blow-up speed in the case when the asymptotic profile is sufficiently regular. These bounds are optimal in dimension $N = 5$. We also prove that if the asymptotic profile is sufficiently regular, then it cannot be strictly negative at the origin.