On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $mathbb {R}^{3 1}$(Memoirs of the American Mathematical Society)

$ \ mathbb {R} ^ {3 1} $中的临界非线性波动方程II型爆破的稳定性

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出版时间
2021年03月30日
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9781470442996
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页      码
267
语      种
英文
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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 2rpartial _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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