Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions

• Published in: Communications in mathematical physics Vol. 327; no. 1; pp. 309 - 332
• Main Authors: Krieger, Joachim, Nakanishi, Kenji, Schlag, Wilhelm
• Format: Journal Article
• Language: English
• 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

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...