TY - JOUR
T1 - Soliton resolution along a sequence of times for the focusing energy critical wave equation
AU - Duyckaerts, Thomas
AU - Jia, Hao
AU - Kenig, Carlos
AU - Merle, Frank
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - In this paper, we prove that any solution of the energy-critical wave equation in space dimensions 3, 4 or 5, which is bounded in the energy space decouples asymptotically, for a sequence of times going to its maximal time of existence, as a finite sum of modulated solitons and a dispersive term. This is an important step towards the full soliton resolution in the nonradial case and without any size restrictions. The proof uses a Morawetz estimate very similar to the one known for energy-critical wave maps, a virial type identity and a new channels of energy argument based on a lower bound of the exterior energy for well-prepared initial data.
AB - In this paper, we prove that any solution of the energy-critical wave equation in space dimensions 3, 4 or 5, which is bounded in the energy space decouples asymptotically, for a sequence of times going to its maximal time of existence, as a finite sum of modulated solitons and a dispersive term. This is an important step towards the full soliton resolution in the nonradial case and without any size restrictions. The proof uses a Morawetz estimate very similar to the one known for energy-critical wave maps, a virial type identity and a new channels of energy argument based on a lower bound of the exterior energy for well-prepared initial data.
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U2 - 10.1007/s00039-017-0418-7
DO - 10.1007/s00039-017-0418-7
M3 - Article
AN - SCOPUS:85023738650
SN - 1016-443X
VL - 27
SP - 798
EP - 862
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 4
ER -