Blow-up bounds under profile approximation for superconformal wave equations
Abstract
For the focusing semilinear wave equation in the superconformal, Sobolev-subcritical range, we prove an upper blow-up bound at the ODE rate near a non-characteristic point, assuming approximation by signed multiples of explicit stationary profiles in similarity variables. The comparison parameters may vary with time, and the error is measured only in a degenerate energy norm on a small extension of the unit ball. The main step is a quantitative exclusion of concentration at the boundary of the profile family. It follows from the nonnegativity of the superconformal Hamza--Zaag energy at admissible vertices and an upper perturbation estimate. We also exclude families with an isolated dominant profile and, under a noncancellation condition, clusters of comparable profiles. For the latter, we derive a limiting energy in RN+1 which accounts for the interactions between profiles.
Related
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BibTeX
@misc{kaabi2026blowup,
title = {{Blow-up bounds under profile approximation for superconformal wave equations}},
author = {Firas Kaabi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26513},
eprint = {2610.26513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26513},
}
RIS
TY - UNPB
TI - Blow-up bounds under profile approximation for superconformal wave equations
AU - Firas Kaabi
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26513
UR - https://arxiv.org/abs/2610.26513
AB - For the focusing semilinear wave equation in the superconformal, Sobolev-subcritical range, we prove an upper blow-up bound at the ODE rate near a non-characteristic point, assuming approximation by signed multiples of explicit stationary profiles in similarity variables. The comparison parameters may vary with time, and the error is measured only in a degenerate energy norm on a small extension of the unit ball. The main step is a quantitative exclusion of concentration at the boundary of the profile family. It follows from the nonnegativity of the superconformal Hamza--Zaag energy at admissible vertices and an upper perturbation estimate. We also exclude families with an isolated dominant profile and, under a noncancellation condition, clusters of comparable profiles. For the latter, we derive a limiting energy in R^N+1 which accounts for the interactions between profiles.
ER -