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

Joachim K Krieger (author)

Softcover

ISBN 10: 147044299X ISBN 13: 9781470442996

Publisher: American Mathematical Society, 2021

Synopsis

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.

About this title

About the Author

Joachim K Krieger, Ecole Polytechnique Federale de Lausanne, Switzerland

Edition details

• Publisher: American Mathematical Society
• Publication date: 2021
• Language: English
• ISBN 10: 147044299X
• ISBN 13: 9781470442996
• Binding: Paperback
• Number of pages: 267