E-raamat: Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\mathbb {R}^{3+1}$

"We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation on constructed in Krieger, Schlag, and Tartaru ("Slow blow-up solutions for the critical focusing semilinear wave equation", 2009) and Krieger and Schlag ("Full range of blow up exponents for the quintic wave equation in three dimensions", 2014) are stable along a co-dimension one Lipschitz manifold of data perturbations in a suitable topology, provided the scaling parameter is sufficiently close to the self-similar rate, i. e., is sufficiently small. This result is qualitatively optimal in light of the result of Krieger, Nakamishi, and Schlag ("Center-stable manifold of the ground state in the energy space for the critical wave equation", 2015). The paper builds on the analysis of Krieger and Wong ("On type I blow-up formation for the critical NLW", 2014)"--

Burzio and Krieger show that the finite time type II blow up solutions for the energy critical nonlinear wave equation on R 2+1 as constructed in Krieger, Schlag, and Tartaro (2009) and in Krieger and Schlag (2014) are stable along a co-dimension-one Lipschitz manifold of data perturbations in a suitable topology under certain conditions. They cover the main theorem and outline of the proof, constructing a two-parameter family of approximate blow up solutions, modulation theory: determining the parameters 1,2, and the iterative construction of a blow up solution almost matching the perturbed initial data. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)