English

On type I blow up formation for the critical NLW

Analysis of PDEs 2014-09-18 v4

Abstract

We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R3+1\mathbb{R}^{3+1}, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger-Nakanishi-Schlag blow-up solutions sitting initially near and "above" the ground state static solution.

Keywords

Cite

@article{arxiv.1301.4378,
  title  = {On type I blow up formation for the critical NLW},
  author = {Joachim Krieger and Willie Wong},
  journal= {arXiv preprint arXiv:1301.4378},
  year   = {2014}
}

Comments

11 pages. Version 3 incorporated suggestions from the referee. The main argument remains unchanged, but the presentation is revised and clarified. Theorem 3.4 (which is an immediately corollary from the method of proof in the original manuscript) is new. Version 4 improved literature review