Profiles for the Radial Focusing 4d Energy-Critical Wave Equation
Name
1402.2307.pdf
Size
645.18 KB
Format
Adobe PDF
Checksum (MD5)
77bb670b7a376ba4b34af65d16bf189d
Author(s)
Côte, R.
Kenig, C. E.
Schlag, W.
Lawrie, Andrew W
Date Issued
December 2017
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Côte, R. et al. “Profiles for the Radial Focusing 4d Energy-Critical Wave Equation.” Communications in Mathematical Physics 357, 3 (December 2017): 943–1008 © 2017 Springer-Verlag
Version
Original manuscript
Abstract
Consider a finite energy radial solution to the focusing energy critical semilinear wave equation in 1 + 4 dimensions. Assume that this solution exhibits type-II behavior, by which we mean that the critical Sobolev norm of the evolution stays bounded on the maximal interval of existence. We prove that along a sequence of times tending to the maximal forward time of existence, the solution decomposes into a sum of dynamically rescaled solitons, a free radiation term, and an error tending to zero in the energy space. If, in addition, we assume that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the case of finite time blow-up) is less than 2 times the critical norm of the ground state solution W, then the decomposition holds without a restriction to a subsequence.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/S00220-017-3043-2
