PreprintCC BY 4.0arXiv
Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS
Abstract
We consider the focusing mass-critical inhomogeneous biharmonic nonlinear Schrödinger equation i∂tu=Δ2u−|x|−b|u|(8−2b)/Nu, 0<b<min{4,N/2}. We prove that every H2(ℝN) solution with negative energy blows up in finite time, both forward and backward. No radial symmetry or finite-variance assumption is required. In particular, this rules out the global grow-up scenario in the previously known negative-energy blow-up alternative and establishes finite-time blow-up in the genuinely nonradial setting. The proof relies on a new localized virial argument exploiting the spatial inhomogeneity to control the localization errors.
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BibTeX
@misc{nguyen2026nonradial,
title = {{Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS}},
author = {Ngoc Uyen Cong Nguyen and Van Duong Dinh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24244},
eprint = {2610.24244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24244},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS
AU - Ngoc Uyen Cong Nguyen
AU - Van Duong Dinh
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24244
UR - https://arxiv.org/abs/2610.24244
AB - We consider the focusing mass-critical inhomogeneous biharmonic nonlinear Schrödinger equation i∂_tu=Δ^2u−|x|^−b|u|^(8−2b)/Nu, 0<b<min{4,N/2}. We prove that every H^2(ℝ^N) solution with negative energy blows up in finite time, both forward and backward. No radial symmetry or finite-variance assumption is required. In particular, this rules out the global grow-up scenario in the previously known negative-energy blow-up alternative and establishes finite-time blow-up in the genuinely nonradial setting. The proof relies on a new localized virial argument exploiting the spatial inhomogeneity to control the localization errors.
ER -