Author

Yi-Lin Song

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Preprint Sep 2026

Global well-posedness and scattering for the defocusing nonlinear Schr\"odinger equation below energy space

In this paper, we prove global well-posedness and scattering below the energy space for the defocusing nonlinear Schr\"odinger equation with intercritical power nonlinearities in spatial dimensions $d\geq3$, improving the regularity threshold of Vi\c{s}an and Zhang [Differ. Integr. Equations, 22(2009), 99-124].

Zu-Yu Ma, Changxing Miao, Yi-Lin Song et al. · 0 citations

Preprint Oct 2026

The quadratic Schr\"odinger system on $\mathbb{T}^6$

In this article, we study the global well-posedness for the quadratic Schr\"odinger system on $\mathbb{T}^6$. To achieve this, we utilize the concentration-compactness/rigitdity argument initiated by Ionescu and Pausader \cite{IPT3}. Our result is also regarded as a periodic analogue of Gao-Meng-Xu-Zheng \cite{GMXZ}.

Yi-Lin Song, Yan Xue, Rui-Xiao Zhang · 0 citations

Preprint Aug 2026

Scattering Theory For 3D Cubic Damped Magnetic Schr\"odinger Equation

We consider the three-dimensional defocusing cubic nonlinear Schr\"odinger equation with variable coefficients, a magnetic potential, and a non-negative localized damping term, \[ i\partial_tu+(\nabla-iA)\cdot G(\nabla-iA)u+ia(x)u=|u|^2u, \qquad t>0,\quad x\in\mathbb R^3. \] No non-trapping condition is imposed on the...

Luca Fanelli, Haruya Mizutani, Yi-Lin Song et al. · 0 citations