On stability of type II blow up for the critical nonlinear wave equation in R3+1
著者
書誌事項
On stability of type II blow up for the critical nonlinear wave equation in R3+1
（Memoirs of the American Mathematical Society, no. 1301）
American Mathematical Society, c2020
- タイトル別名
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On stability of type 2 blow up for the critical nonlinear wave equation in R3+1
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注記
"September 2020, volume 267, number 1301 (fifth of 7 numbers)"
Includes bibliographical reference (p. 127-129)
内容説明・目次
内容説明
The author shows that the finite time type II blow up solutions for the energy critical nonlinear wave equation $ \Box u = -u^5 $ on $\mathbb R^3+1$ constructed in Krieger, Schlag, and Tataru (2009) and Krieger and Schlag (2014) are stable along a co-dimension three manifold of radial data perturbations in a suitable topology, provided the scaling parameter $\lambda (t) = t^-1-\nu $ is sufficiently close to the self-similar rate, i. e. $\nu >0$ is sufficiently small. Our method is based on Fourier techniques adapted to time dependent wave operators of the form $ -\partial _t^2 + \partial _r^2 + \frac 2r\partial _r +V(\lambda (t)r) $ for suitable monotone scaling parameters $\lambda (t)$ and potentials $V(r)$ with a resonance at zero.
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