13 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…
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 asympto…
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 in dimensions $d=…