18 citations · 41 across the 20 of their papers we have counts for
22 papers
Global well-posedness and scattering for the three-dimensional defocusing cubic Schrödinger equation in ,
Qingtang Su, Zehua Zhao
We prove global well-posedness and scattering for the three-dimensional defocusing cubic nonlinear Schrödinger equation with arbitrary initial data in , ,…
On Strichartz estimates for many-body Schrödinger equation in the periodic setting
Xiaoqi Huang, Xueying Yu, Zehua Zhao +1
In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori , where . The results hold for…
On well-posedness results for the cubic-quintic NLS on
Yongming Luo, Xueying Yu, Haitian Yue +1
We consider the periodic cubic-quintic nonlinear Schrödinger equation \begin{align}\label{cqnls_abstract} (i\partial_t +Δ)u=μ_1 |u|^2 u+μ_2 |u|^4 u\tag{CQNLS} \end{align} on the th…
On Strichartz estimate for many body Schrödinger equation in the waveguide setting
Zehua Zhao
In this short paper, we prove Strichartz estimates for N-body Schrödinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces …
On decaying properties of nonlinear Schrödinger equations
Chenjie Fan, Gigliola Staffilani, Zehua Zhao
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schrödinger equation with various initial data, deterministic a…
On scattering asymptotics for the 2D cubic resonant system
Kailong Yang, Zehua Zhao
In this paper, we prove scattering asymptotics for the 2D (discrete dimension) cubic resonant system. This scattering result was used in Zhao \cite{Z1} as an assumption to obtain t…
Singular Levy processes and dispersive effects of generalized Schrödinger equations
Yannick Sire, Xueying Yu, Haitian Yue +1
We introduce new models for Schrödinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to under…
A note on decay property of nonlinear Schrödinger equations
Chenjie Fan, Zehua Zhao
In this note, we show the existence of a special solution to defocusing cubic NLS in , which lives in for all , but scatters to a linear solution in a very slo…
On the decay property of the cubic fourth-order Schrödinger equation
Xueying Yu, Haitian Yue, Zehua Zhao
In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on () enjoys the same (pointwise) decay proper…
Long time behavior of stochastic NLS with a small multiplicative noise
Chenjie Fan, Weijun Xu, Zehua Zhao
We prove the global space-time bound for the mass critical nonlinear Schrödinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering be…
Global Well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we study the well-posedness theory and the scattering asymptotics for fourth-order Schrödinger equations (4NLS) on waveguide manifolds (semiperiodic spaces) $\mathbb…
On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise
Chenjie Fan, Zehua Zhao
In this article, we study Stochastic mass critical nonlinear Schrödinger equations with a multiplicative noise in 3D with a slight time decay (), and prove…
Global Well-posedness for the focusing cubic NLS on the product space
Xueying Yu, Haitian Yue, Zehua Zhao
In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space with initial data bel…
Decay estimates for nonlinear Schrödinger equations
Chenjie Fan, Zehua Zhao
In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, 3d cubic and 2d quintic NLS (nonlinear Schrödinger equations).
Global estimates for the Hartree-Fock-Bogoliubov equations
Jacky Jia Wei Chong, Manoussos G. Grillakis, Matei Machedon +1
We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and . This allows one to extend the local exi…
Long time dynamics for defocusing cubic NLS on three dimensional product space
Zehua Zhao, Jiqiang Zheng
In this article, we study long time dynamics for defocusing cubic NLS on three dimensional product space. First, we apply the decoupling method in Bourgain-Demeter \cite{BD} to est…
Well-posedness for energy-critical nonlinear Schrödinger equation on waveguide manifold
Xing Cheng, Zehua Zhao, Jiqiang Zheng
In this article, we utilize the scale-invariant Strichartz estimate on waveguide which is developed recently by Barron \cite{Barron} based on Bourgain-Demeter decoupling meth…
Dynamics of subcritical threshold solutions for energy-critical NLS
Qingtang Su, Zehua Zhao
In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on () with nonradial data. This problem with radial…
On scattering for the defocusing high dimensional inter-critical NLS
Chuanwei Gao, Zehua Zhao
In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schr{ö}dinger equation with critical index satisfying when …
On scattering for the defocusing quintic nonlinear Schrödinger equation on the two-dimensional cylinder
Xing Cheng, Zihua Guo, Zehua Zhao
In this article, we prove the scattering for the quintic defocusing nonlinear Schrödinger equation on cylinder in . We establish an abstract lin…
On scattering for the defocusing nonlinear Schrödinger equation on waveguide (when )
Zehua Zhao
In the article, we prove the large data scattering for two problems, i.e. the defocusing quintic nonlinear Schr{ö}dinger equation on and the de…
Global well-posedness and scattering for the defocusing cubic Schrödinger equation on waveguide
Zehua Zhao
We consider the problem of large data scattering for the defocusing cubic nonlinear Schrödinger equation on . This equation is critical both a…