Jiqiang Zheng

activity

20062026

most citedFocusing NLS with inverse square potential

41 citations · 357 across the 68 of their papers we have counts for

collaborators

69 papers

cs.SE2026

When Messages Go Wrong: Understanding Communication Faults in LLM-Based Multi-Agent Systems

Jinhao Zhou, Xiaoyu Zhang, Jiongchi Yu +2

LLM-based multi-agent systems (LLM-MAS) use specialized agents that exchange messages to accomplish complex tasks. Their reliance on networked protocols, remote tools, and model en…

math.AP2026

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\…

math.AP2026

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)…

math.AP2026

Threshold dynamics for the 4 $d$ mass-energy double critical NLS

Alex H. Ardila, Zuyu Ma, Jason Murphy +1

We consider the 4 $d$ mass-energy double critical NLS \[ (i\partial_t+Δ)u = -|u|^2 u + |u| u. \] In Luo (2024) and Cheng--Miao--Zhao (2016), the authors established a scattering/blo…

math.AP2025

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…

math.AP2025

Bochner-Riesz means on a conical singular manifold

Qiuye Jia, Junyong Zhang, Jiqiang Zheng

We prove a sharp $L^{p}$ -boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0, \infty) \times S_{σ}^{1}$ . The operator $S_{λ}^{δ} (Δ_{X})$ is bounded on $L^{p} (X)$ fo…

math.AP2025

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $R^{2}$

Huanqing Guo, Junyong Zhang, Jiqiang Zheng

This paper studies the sharp $L^{p}$ - $L^{q}$ boundedness of the Bochner-Riesz operator $S_{λ}^{δ} (L_{A})$ associated with a scaling-critical magnetic Schrödinger operato…

math.AP2025

$L^{p}$ -estimates for the 2D wave equation in the scaling-critical magnetic field

Jialu Wang, Fang Zhang, Junyong Zhang +1

In this paper, we study the $L^{p}$ -estimates for the solution to the $2 D$ -wave equation with a scaling-critical magnetic potential. Inspired by the work of \cite{FZZ}, we…

math.AP2024

Modified scattering for the cubic dispersion-managed NLS

Jason Murphy, Jiqiang Zheng

We establish a small-data modified scattering result for the $1 d$ cubic dispersion-managed NLS (with time-dependent dispersion map) for initial data in a weighted space.

math.AP2024

Global well-posedness and scattering for mass-critical inhomogeneous NLS when $d \geq 3$

Xuan Liu, Changxing Miao, Jiqiang Zheng

We prove global well-posedness and scattering for solutions to the mass-critical inhomogeneous nonlinear Schrödinger equation $i \partial_{t} u + Δ u = \pm ∣ x ∣^{- b} ∣ u ∣^{\frac{4 - 2 b}{d}} u$ …

math.AP2024

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…

math.AP2024

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…

math.AP2024

Dynamics of the combined nonlinear Schrödinger equation with inverse-square potential

Zuyu Ma, Yilin Song, Jiqiang Zheng

We consider the long-time dynamics of focusing energy-critical Schrödinger equation perturbed by the $H ˙^{\frac{1}{2}}$ -critical nonlinearity and with inverse-square potential(C…

math.AP2024

Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders

Xing Cheng, Jiqiang Zheng

In this article, we consider the nonlinear Schrödinger equation on the cylinder $R^{d} \times T$ . In the long range case, we show there is no linear scattering state…

math.AP2024

On bilinear Strichartz estimates on waveguides with applications

Yangkendi Deng, Chenjie Fan, Kailong Yang +2

We study local-in-time and global-in-time bilinear Strichartz estimates for the Schrödinger equation on waveguides. As applications, we apply those estimates to study global well-p…

math.AP2023

Restriction estimates for one class of hypersurfaces with vanishing curvature in $R^{n}$

Zhuoran Li, Jiqiang Zheng

In this paper, we study the restriction problem for one class of hypersurfaces with vanishing curvature in $R^{n}$ with $n$ being odd. We obtain an $L^{2} - L^{p}$ restriction est…

math.AP2023

Threshold dynamics for the 3 $d$ radial NLS with combined nonlinearity

Alex H. Ardila, Jason Murphy, Jiqiang Zheng

We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+Δ)u = |u|^2 u - |u|^4 u. \] In [18…

math.AP2023

Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential

Mingming Deng, Xiaoyan Su, Jiqiang Zheng

In this paper, we study the $2$ D cubic nonlinear Schrödinger equation (NLS) with the partial harmonic potential. First, we prove the local well-posedness in Bourgain spaces by esta…

math.AP2023

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 $T^{d}$ , where $d \geq 3$ . The results hold for…

math.AP2022

Decoupling for finite type phases in higher dimensions

Chuanwei Gao, Zhuoran Li, Tengfei Zhao +1

In this paper, we establish an $ℓ^{2}$ decoupling inequality for the hypersurface \[\Big\{(ξ_1,...,ξ_{n-1},ξ_1^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\}\]associate…

math.AP2021

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

Xiaofen Gao, Junyong Zhang, Jiqiang Zheng

We study the dispersive behaviors of two-particles Schrödinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schrödinger and w…

math.AP2021★ 15 cited

The $W^{s, p}$ -boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

Changxing Miao, Xiaoyan Su, Jiqiang Zheng

In this paper, we investigate the $W^{s, p}$ -boundedness for stationary wave operators of the Schrödinger operator with inverse-square potential $$\mathcal L_a=-Δ+\tfrac{a}{|x|^2},…

math.AP2021

$ℓ^{2}$ decoupling for certain surfaces of finite type in $R^{3}$

Zhuoran Li, Jiqiang Zheng

In this article, we establish an $ℓ^{2}$ decoupling inequality for the surface $F_{4}^{2} := {(ξ_{1}, ξ_{2}, ξ_{1}^{4} + ξ_{2}^{4}) : (ξ_{1}, ξ_{2}) \in [0, 1]^{2}}$ associated with the decompositio…

math.AP2021

Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

Luca Fanelli, Junyong Zhang, Jiqiang Zheng

We study the $L^{p} - L^{q}$ -type uniform resolvent estimates for 2D-Schrödinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an…

When Messages Go Wrong: Understanding Communication Faults in LLM-Based Multi-Agent Systems

Scattering Theory For 3D Cubic Damped Magnetic Schrödinger Equation

Generic ill-posedness for Schrödinger equation with power-type nonlinearity on S2

Threshold dynamics for the 4d mass-energy double critical NLS

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

Bochner-Riesz means on a conical singular manifold

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in R2

Lp-estimates for the 2D wave equation in the scaling-critical magnetic field

Modified scattering for the cubic dispersion-managed NLS

Global well-posedness and scattering for mass-critical inhomogeneous NLS when d≥3

Improved global well-posedness for the cubic NLS on two-dimensional waveguide $\R\times\T$

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

Dynamics of the combined nonlinear Schrödinger equation with inverse-square potential

Remark on the scattering theory of the nonlinear Schrödinger equation on the cylinders

On bilinear Strichartz estimates on waveguides with applications

Restriction estimates for one class of hypersurfaces with vanishing curvature in Rn

Threshold dynamics for the 3d radial NLS with combined nonlinearity

Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential

On Strichartz estimates for many-body Schrödinger equation in the periodic setting

Decoupling for finite type phases in higher dimensions

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

The Ws,p-boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

ℓ2 decoupling for certain surfaces of finite type in R3

Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

Generic ill-posedness for Schrödinger equation with power-type nonlinearity on $S^{2}$

Threshold dynamics for the 4 $d$ mass-energy double critical NLS

Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in $R^{2}$

$L^{p}$ -estimates for the 2D wave equation in the scaling-critical magnetic field

Global well-posedness and scattering for mass-critical inhomogeneous NLS when $d \geq 3$

Restriction estimates for one class of hypersurfaces with vanishing curvature in $R^{n}$

Threshold dynamics for the 3 $d$ radial NLS with combined nonlinearity

The $W^{s, p}$ -boundedness of stationary wave operators for the Schrödinger operator with inverse-square potential

$ℓ^{2}$ decoupling for certain surfaces of finite type in $R^{3}$