On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $/mathbb {R}^{3+1}$
Seiten
2021
American Mathematical Society (Verlag)
978-1-4704-4299-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4299-6 (ISBN)
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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.
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.
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.
Joachim K Krieger, Ecole Polytechnique Federale de Lausanne, Switzerland
| Erscheinungsdatum | 02.11.2020 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 260 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-4299-X / 147044299X |
| ISBN-13 | 978-1-4704-4299-6 / 9781470442996 |
| Zustand | Neuware |
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