Yilin Song

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 $S^{2}$

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 $S^{2}$ : \begin{align*} i\partial_tu+Δ_{g}u=F(u)…

Geometric uncertainty principles for Schrödinger evolutions on negatively curved manifolds

Changxing Miao, Yilin Song, Ruihan Zhou

In this paper, we study the uncertainty principle for Schrödinger equations with a bounded time-independent potentials on certain Cartan-Hadamard manifolds endowed with an asymptot…

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…

Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

Zuyu Ma, Yilin Song, Kai Yang +1

We study the threshold scattering problem for the energy-critical nonlinear Schrödinger equation with a repulsive inverse-square potential $\frac{a}{∣ x ∣ ^{2}} > 0$ in dimensions $d= 4…

On the pointwise convergence of NLS flow on $§^{2}$

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 $S^{2}$ , \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,…

Control and stabilization problem for a class of fourth-order nonlinear Schrödinger equation on boundaryless compact manifold

Yilin Song, Jiqiang Zheng, Ruihan Zhou

In this paper, we study the stabilization property and large time controllability for a class of fourth-order Schrödinger equations on a compact manifold without boundary in dimens…

Asymptotic behavior of mass-critical Schrödinger equation in $R$

Fanfei Meng, Yilin Song, Ruixiao Zhang

In this paper, we study the long-time behavior for the mass-critical nonlinear Schrödinger equation on the line \[ i\partial_t u + \partial_x^2 u = |u|^4 u, u(0, x) = u_0 \in L_x^2…

On Growth of Sobolev norms for cubic Schrödinger equation with harmonic potential in dimensions $d = 2, 3$

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 $i u_{t} + Δ_{Ω} u = ∣ u ∣^{α} u$ in the exterior domain $Ω$ of…

Global well-posedness for the defocusing cubic nonlinear Schrödinger equation on $T^{3}$

Yilin Song, Ruixiao Zhang

In this article, we investigate the global well-posedness for the defocusing, cubic nonlinear Schrödinger equation posed on $\T^3$ with intial data lying in its critical space $H^\…

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+Δ_{\R\times\T…

On scattering for two-dimensional quintic Schrödinger equation under partial harmonic confinement

Zuyu Ma, Yilin Song, Ruixiao Zhang +2

In this article, we study the scattering theory for the two dimensional defocusing quintic nonlinear Schrödinger equation(NLS) with partial harmonic oscillator which is given by \b…

Global well-posedness for rough solutions of defocusing cubic NLS on three dimensional compact manifolds

Chen Qionglei, Yilin Song, Jiqiang Zheng

In this article, we investigate the global well-posedness for cubic nonlinear Schrödinger equation(NLS) $i \partial_{t} u + Δ_{g} u = ∣ u ∣^{2} u$ posed on the three dimensional compact manifolds…