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Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R
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 expo...
Enregistré dans:
| Auteurs principaux : | , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R / Stefano Burzio, Joachim Krieger |
| Publié : |
Providence (R.I.) :
American Mathematical Society
, C 2022 |
| Description matérielle : | 1 vol. (III-75 p.) |
| Collection : | Memoirs of the American Mathematical Society ; 1369 |
| Sujets : |
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| 200 | 1 | |a Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R |f Stefano Burzio, Joachim Krieger | |
| 214 | 0 | |a Providence (R.I.) |c American Mathematical Society | |
| 214 | 4 | |d C 2022 | |
| 215 | |a 1 vol. (III-75 p.) |c illustrations |d 26 cm | ||
| 225 | 0 | |a Memoirs of the American Mathematical Society |x 0065-9266 |v number 1369 | |
| 300 | |a "July 2022, volume 278, number 1369 (fourth of 6 numbers)." | ||
| 320 | |a Bibliogr. p. 71-74. Index | ||
| 330 | |a 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) |2 résumé des auteurs | ||
| 359 | 2 | |b The main theorem and outline of the proof |b Construction of a two parameter family of approximate blow up solutions |b Modulation theory; determination of the parameters [gamma]1,2. |b Iterative construction of blow up solution almost matching the perturbed initial data |b Proof of theorem 2.1 |b Outlook | |
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