10 papers
Scattering Theory For 3D Cubic Damped Magnetic Schrödinger Equation
Luca Fanelli, Haruya Mizutani, Yilin Song +2
We consider the three-dimensional defocusing cubic nonlinear Schrödinger equation with variable coefficients, a magnetic potential, and a non-negative localized damping term, \[ i\…
Generic ill-posedness for Schrödinger equation with power-type nonlinearity on
Sijie Qian, Yilin Song, Ruixiao Zhang +1
In this article, we investigate the local well-posedness of the nonlinear Schrödinger equation on the two-dimensional sphere : \begin{align*} i\partial_tu+Î_{g}u=F(…
Improved global well-posedness for the cubic NLS on two-dimensional waveguide $\R\times\T$
Qionglei Chen, Yilin Song, Kailong Yang +2
In this article, we show that the solution to defocusing cubic nonlinear Schrödinger equation (NLS) posed on the two-dimensional waveguide \begin{align*} i\partial_tu+Î_{\R\times…
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 + Î_g u = |u|^2u, \…
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+Î_{z}u-y^2 u =- |u|^…