Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions

For the critical focusing wave equation □ u = u 5 on R 3 + 1 in the radial case, we establish the role of the “center stable” manifold Σ constructed in Krieger and Schlag (Am J Math 129(3):843–913, 2007 ) near the ground state ( W , 0) as a threshold between blowup and scattering to zero, establishi...

Full description

Saved in:
Bibliographic Details
Published inCommunications in mathematical physics Vol. 327; no. 1; pp. 309 - 332
Main Authors Krieger, Joachim, Nakanishi, Kenji, Schlag, Wilhelm
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014
Subjects
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Limit Absorption Principle
Invariant Manifold
Nonlinear Wave Equation
Wave Equation
Bootstrap Assumption
Online AccessGet full text

Cover

More Information
Summary:For the critical focusing wave equation □ u = u 5 on R 3 + 1 in the radial case, we establish the role of the “center stable” manifold Σ constructed in Krieger and Schlag (Am J Math 129(3):843–913, 2007 ) near the ground state ( W , 0) as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizoń et al. (Nonlinearity 17(6):2187–2201, 2004 ). The underlying topology is stronger than the energy norm.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-1900-9