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L∞-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability
Abstract
We study a generalized Gross-Pitaevskii equation arising in the mean-field description of exciton-polariton Bose-Einstein condensates. The dynamics close to macroscopic wave functions r0eiω0 t +ik0x is governed by a stabilizing relaxation mechanism without suppressing dispersive blow-up. We show that this competition yields L∞-regularity thresholds. More precisely, we construct solutions for which arbitrarily small perturbations from C4b can develop finite time blow-up in C3b whereas perturbations from C4+ηb for every η>0, satisfy a global-in-time C3b-stability estimate. The stability analysis is carried out in modulation spaces M∞,1k.
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BibTeX
@misc{alexopoulos2026lregularity,
title = {{$L^\infty$-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability}},
author = {Joannis Alexopoulos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20888},
eprint = {2610.20888},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20888},
}
RIS
TY - UNPB
TI - L^∞-regularity thresholds for a generalized Gross-Pitaevskii equation: dispersive blow-up vs. nonlinear stability
AU - Joannis Alexopoulos
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20888
UR - https://arxiv.org/abs/2610.20888
AB - We study a generalized Gross-Pitaevskii equation arising in the mean-field description of exciton-polariton Bose-Einstein condensates. The dynamics close to macroscopic wave functions r_0e^iω_0 t +ik_0x is governed by a stabilizing relaxation mechanism without suppressing dispersive blow-up. We show that this competition yields L^∞-regularity thresholds. More precisely, we construct solutions for which arbitrarily small perturbations from C^4_b can develop finite time blow-up in C^3_b whereas perturbations from C^4+η_b for every η>0, satisfy a global-in-time C^3_b-stability estimate. The stability analysis is carried out in modulation spaces M_∞,1^k.
ER -