7 papers
Magnetic uncertainty in variable geometry
Luca Fanelli, Yilin Song, Ying Wang +2
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence o…
On the pointwise convergence of NLS flow on
Fanfei Meng, Yilin Song, Chenmin Sun +2
In this paper, we study the almost everywhere convergence of the cubic nonlinear Schrödinger flow to the initial data on , \begin{equation*} iu_t + Δ_g u = |u|^2u, \qu…
Dynamics of focusing nonlinear Schrödinger equation with partial harmonic confinement in higher dimensions
Tianhao Liu, Zuyu Ma, Yilin Song +1
We study the following focusing intercritical nonlinear Schrödinger equation with partial harmonic confinement: \begin{equation*} \begin{cases} i\partial_t u+Δ_{z}u-y^2 u =- |u|^αu…
A Paley-Wiener type uniqueness result for the electromagnetic Schrödinger equation
Yilin Song, Ying Wang, Jiqiang Zheng +1
In this paper, we establish a Paley-Wiener type uncertainty principle for Schrödinger equations with bounded electric and magnetic potentials, \begin{align*} i\partial_tu+Δ_Au+V(t,…
On Growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions
Yilin Song, Ruixiao Zhang, Jiqiang Zheng
In this article, we study the growth of higher-order Sobolev norms for solutions to the defocusing cubic nonlinear Schrödinger equation with harmonic potential in dimensions $d=2,3…
Scattering theory for the defocusing 3d NLS in the exterior of a strictly convex obstacle
Xuan Liu, Yilin Song, Jiqiang Zheng
In this paper, we investigate the global well-posedness and scattering theory for the defocusing nonlinear Schrödinger equation in the exterior domain of…