Soliton resolution for the radial quadratic wave equation in six space dimensions
Charles Collot, Thomas Duyckaerts, Carlos Kenig, Frank Merle
备注：
In this version 2, the article has been shortened in comparison with version 1. Version 2 only keeps the main theorems and their proofs. The results of Section 3, as well as the results of Section 4 and 5, of version 1, have been extended and are now contained in two other articles, see arXiv preprint arXiv:2211.16075 and arXiv:2211.16085 respectively
We consider the quadratic semilinear wave equation in six dimensions. This energy critical problem admits a ground state solution, which is the unique (up to scaling) positive stationary solution. We prove that any spherically symmetric solution, that remains bounded in the energy norm, evolves asymptotically to a sum of decoupled modulated ground states, plus a radiation term. As a by-product of the approach we prove the non-existence of multisoliton solutions that do not emit any radiation. The proof follows the method initiated for large odd dimensions by the last three authors, reducing the problem to ruling out the existence of such non-radiative multisolitons, by deriving a contradiction from a finite dimensional system of ordinary differential equations governing their modulation parameters. In comparison, the difficulty in six dimensions is the failure of certain channel of energy estimates and the related existence of a linear resonance. The main novelties are the use of new channel of energy estimates, as well as the classification of non-radiative solutions with small energy.
Blow-up dynamics for radial self-dual Chern-Simons-Schrödinger equation with prescribed asymptotic profile
Seoul National University（首尔大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；UC Berkeley（加州大学伯克利分校）；Korea Institute for Advanced Study（韩国高等研究院）
Finite-mass soliton-type rigidity and four-channel reduction for the three-dimensional nonradial focusing energy-critical nonlinear Schrödinger equation
Guangdong University of Education（广东教育学院）；University of Louisville（路易斯维尔大学）
