no. 2
Instability of type II blow up for the quintic nonlinear wave equation on ℝ3+1
[Instabilité d'explosion de type II pour l'équation des ondes non-linéaire de degré 5 sur ℝ3+1]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 339-355

We prove that the blow up solutions of type II character constructed by Krieger-Schlag-Tataru [10] as well as Krieger-Schlag [9] are unstable in the energy topology in that there exist open data sets whose closure contains the data of the preceding type II solutions and such that data in these sets lead to solutions scattering to zero at time t=+∞.

On montre que les solutions explosives de type II construites par Krieger-Schlag-Tataru [9] sont instables dans l'espace d'énergie au sens qu'il existe des ensembles ouverts de données initiales dont la fermeture contient les données initiales des solutions de type II et telles que les solutions correspondantes existent globalement en temps positif et s'évanouissent vers t=+∞.

Publié le :
DOI : 10.24033/bsmf.2690
Classification : 35L05, 35B40
Keywords: Critical wave equation, hyperbolic dynamics, blowup, scattering, stability, invariant manifold
Mots-clés : Équation d'onde critique, dynamique hyperbolique, explosion de solutions, scattering, stabilité, variété invariante 
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     author = {Krieger, Joachim and Nahas, Joules},
     title = {Instability of type {II} blow up for the quintic nonlinear wave equation on $\mathbb {R}^{3+1}$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {339--355},
     year = {2015},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {2},
     doi = {10.24033/bsmf.2690},
     mrnumber = {3351183},
     zbl = {1320.35220},
     language = {en},
     url = {https://numdam.org/articles/10.24033/bsmf.2690/}
}
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Krieger, Joachim; Nahas, Joules. Instability of type II blow up for the quintic nonlinear wave equation on $\mathbb {R}^{3+1}$. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 339-355. doi: 10.24033/bsmf.2690

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