bokomslag On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $\mathbb {R}^{3+1}$
Vetenskap & teknik

On Stability of Type II Blow Up for the Critical Nonlinear Wave Equation in $\mathbb {R}^{3+1}$

Joachim K Krieger

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  • 267 sidor
  • 2021
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.
  • Författare: Joachim K Krieger
  • Format: Pocket/Paperback
  • ISBN: 9781470442996
  • Språk: Engelska
  • Antal sidor: 267
  • Utgivningsdatum: 2021-03-30
  • Förlag: American Mathematical Society