Shijun Zheng

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math.AP2025

Blowup rate for rotational NLS with a repulsive potential

Yi Hu, Yongki Lee, Shijun Zheng

In this paper we give an analytical proof of the `` $lo g$ - $lo g$ '' blowup rate for mass-critical nonlinear Schrödinger equation (NLS) with a rotation ( $Ω \neq = 0$ ) and a repulsive ha…

math.AP2025

Perturbed Fourier Transform Associated with Schrödinger Operators

Shijun Zheng

We give an exposition on the $L^{2}$ theory of the perturbed Fourier transform associated with a Schrödinger operator $H = - d^{2} / d x^{2} + V$ on the real line, where $V$ is a real-valued \m…

math.AP2024

Existence and non-existence of ground state solutions for magnetic NLS

Oleg Asipchuk, Christopher Leonard, Shijun Zheng

We show the existence and stability of ground state solutions (g.s.s.) for $L^{2}$ -critical magnetic nonlinear Schrödinger equations (mNLS) for a class of unbounded electromagnetic p…