Stability of slow blow-up solutions for the critical focussing nonlinear wave equation on  $\mathbb{R}^{3+1}$

In this brief survey we outline the recent advances on the stability issues of certain finite time type II blow-up solutions for the energy critical focusing wave equation $\Box u=-u^{5}$ in $\mathbb{R}^{3+1}$. Hereafter we use the convention $\Box=-\partial^{2}_{t}+\triangle$. The objective of this article is twofold: firstly we describe the construction of singular solutions contained in \cite{krieger2009slow} and \cite{krieger2014full}, and secondly we undertake a detailed analysis of its stability properties enclosed in \cite{krieger2017stability} and \cite{krieger2017optimal}.