A universal bound on the blow-up rate for the focusing mass-critical nonlinear Schr\"odinger equation

Beomjong Kwak; Soonsik Kwon

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arXiv · 2602.21968

A universal bound on the blow-up rate for the focusing mass-critical nonlinear Schr\"odinger equation

Beomjong Kwak·Soonsik Kwon

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Abstract

In this paper, we investigate a universal blow-up bound for the focusing mass-critical nonlinear Schr\"odinger equation for general initial data in $L^2(\mathbb R^d)$, extending previous knowledge for mass near the ground-state threshold due to Merle and Rapha\"el. The main results are twofold. First, we show the nonexistence of self-similar rate blow-up solutions. Second, under radial symmetry, we establish the sharp log--log correction to the self-similar bound on the blow-up rate. The proofs are based on a new analysis of general blow-up solutions, which does not rely on any ansatz or variational structure.

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Beomjong Kwak, Soonsik Kwon. 2026-02-25. A universal bound on the blow-up rate for the focusing mass-critical nonlinear Schr\"odinger equation. https://arxiv.org/abs/2602.21968

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