Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R^{3+1}

Stefano Burzio; Joachim Krieger

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arXiv · 1709.06408

Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R^{3+1}

Stefano Burzio·Joachim Krieger

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Abstract

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation \[ \Box u = -u^5 \] on $\mathbb R^{3+1}$ constructed by Krieger-Schlag-Tataru are stable along a co-dimension one Lipschitz manifold of data perturbations in a suitable topology, provided the scaling parameter $\lambda(t) = t^{-1-\nu}$ is sufficiently close to the self-similar rate, i. e. $\nu>0$ is sufficiently small. This result is qualitatively optimal in light of a result by Krieger-Nakanishi-Schlag. The paper builds on the analysis in an earlier paper by the second author.

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Stefano Burzio, Joachim Krieger. 2017-09-19. Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R^{3+1}. https://arxiv.org/abs/1709.06408

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