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On 2D Scattering for a Critical Nonlinear Schrödinger Flow
Abstract
We study modified scattering for the two-dimensional defocusing nonlinear Schrödinger equation (NLS) with the gauge-invariant, scattering-critical nonlinearity |u|u. We prove that the remodulated interaction representation has a local L2 limit for general data in Σ=H1∩F−1H1. For radial data, we prove convergence in Lp(R2) for every 2<p<∞.
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BibTeX
@misc{georgiev2026scattering,
title = {{On 2D Scattering for a Critical Nonlinear Schrödinger Flow}},
author = {Vladimir Georgiev and Tohru Ozawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08845},
eprint = {2609.08845},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08845},
}
RIS
TY - UNPB
TI - On 2D Scattering for a Critical Nonlinear Schrödinger Flow
AU - Vladimir Georgiev
AU - Tohru Ozawa
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08845
UR - https://arxiv.org/abs/2609.08845
AB - We study modified scattering for the two-dimensional defocusing nonlinear Schrödinger equation (NLS) with the gauge-invariant, scattering-critical nonlinearity |u|u. We prove that the remodulated interaction representation has a local L^2 limit for general data in Σ=H^1∩F^−1H^1. For radial data, we prove convergence in L^p(R^2) for every 2<p<∞.
ER -