Instability of type II blow up for the quintic nonlinear wave equation on \R^{3+1}

TL;DR

This paper demonstrates the instability of certain finite time blow-up solutions for the quintic nonlinear wave equation in four-dimensional space, showing that nearby initial data can lead to solutions that scatter to zero.

Contribution

It proves the instability of type II blow-up solutions in the energy topology and constructs open data sets leading to scattering solutions.

Findings

Type II blow-up solutions are unstable in the energy topology.

Open sets of initial data can lead to solutions scattering to zero.

Blow-up solutions are in the closure of these open data sets.

Abstract

We prove that the finite time blow up solutions of type II character constructed by Krieger-Schlag-Tataru as well as Krieger-Schlag are unstable in the energy topology, in that there exist open data sets in the energy topology containing these blow up solutions in their closure and which lead to solutions scattering to zero at time infinity.