We analyse the energy supercritical semilinear wave equation
in space. We first prove in a suitable regime of parameters the existence of a countable family of self-similar profiles which bifurcate from the soliton solution. We then prove the non-radial finite codimensional stability of these profiles by adapting the functional setting of [22].
Nous analysons l’équation d’onde semi-linéaire supercritique en énergie
dans l’espace . Nous prouvons d’abord, dans un régime approprié de paramètres, l’existence d’une famille dénombrable de profils auto-similaires qui bifurquent à partir de la solution du soliton. Nous prouvons ensuite la stabilité non radiale en codimension finie de ces profils en adaptant le cadre fonctionnel de [22].
Accepted:
Published online:
Keywords: Semi-linear wave equation, self-similar solution, blow up, focusing, energy super-critical, finite codimensional stability
Mot clés : Équation d’onde semi-linéaire, solution auto-similaire, explosion, supercritique en énergie, stabilité en codimension finie
Jihoi Kim 1
@article{JEP_2024__11__1483_0, author = {Jihoi Kim}, title = {On self-similar blow up for the~energy~supercritical semilinear wave~equation}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {1483--1542}, publisher = {\'Ecole polytechnique}, volume = {11}, year = {2024}, doi = {10.5802/jep.282}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.282/} }
TY - JOUR AU - Jihoi Kim TI - On self-similar blow up for the energy supercritical semilinear wave equation JO - Journal de l’École polytechnique — Mathématiques PY - 2024 SP - 1483 EP - 1542 VL - 11 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.282/ DO - 10.5802/jep.282 LA - en ID - JEP_2024__11__1483_0 ER -
%0 Journal Article %A Jihoi Kim %T On self-similar blow up for the energy supercritical semilinear wave equation %J Journal de l’École polytechnique — Mathématiques %D 2024 %P 1483-1542 %V 11 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.282/ %R 10.5802/jep.282 %G en %F JEP_2024__11__1483_0
Jihoi Kim. On self-similar blow up for the energy supercritical semilinear wave equation. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1483-1542. doi : 10.5802/jep.282. https://jep.centre-mersenne.org/articles/10.5802/jep.282/
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