Soliton resolution along a sequence of times for the focusing energy critical wave equation

TL;DR

This paper proves the soliton resolution conjecture for general type II solutions to the focusing energy critical wave equation in dimensions 3 to 5 along a sequence of times, advancing understanding of wave behavior.

Contribution

It extends previous work by establishing soliton resolution for nonradial solutions without size restrictions, covering a broader class of solutions in higher dimensions.

Findings

Proves soliton resolution for type II solutions in dimensions 3-5.

Extends previous results to nonradial solutions without size restrictions.

Progresses towards full soliton resolution in the nonradial case.

Abstract

In this paper, we prove the soliton resolution conjecture for general type II solutions to the focusing energy critical wave equation, in space dimension 3,4 or 5, along a sequence of times. This is an important step towards the full soliton resolution in the nonradial case and without any size restrictions. This paper is an extension of the arXiv preprint 1510:00075 by the second author, where the finite time blow-up case is treated, with an error converging to zero in a weaker sense.