10 papers
A sharp isoperimetric bound for the ratio of the fifth and fourth eigenvalues of Dirichlet Laplacian
Zhen Song, Ruixiao Zhang
Let be a bounded domain with . The well-known Payne-Pólya-Weinberger conjecture for consecutive eigenvalue ratios asserts that $$ \frac{λ_{m+1}(Ω)}{λ…
The quadratic Schrödinger system on
Yilin Song, Yan Xue, Ruixiao Zhang
In this article, we study the global well-posedness for the quadratic Schrödinger system on . To achieve this, we utilize the concentration-compactness/rigitdity argu…
Bilinear estimates for Schrödinger equation with repulsive inverse-square potential and its application
Mingming Deng, Yilin Song, Ruixiao Zhang
In this paper, we establish the bilinear Strichartz estimates for the following linear Schrödinger equation with repulsive inverse-square potential $i\partial_tu+\La u=0$ where $\L…
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+Δ_{g}u=F(u)…
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…
Asymptotic behavior of mass-critical Schrödinger equation in
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
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…
Global well-posedness for the defocusing cubic nonlinear Schrödinger equation on
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…