Items related to On Stability of Type II Blow Up for the Critical Nonlinear...

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)

 
9781470442996: 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
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.

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About the Author

Joachim K Krieger, Ecole Polytechnique Federale de Lausanne, Switzerland

"About this title" may belong to another edition of this title.

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