9 papers
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…
Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
Alex H. Ardila, Zuyu Ma, Ying Wang
We consider the focusing cubic nonlinear Schrodinger equation with a repulsive inverse-power potential , where and . At the mass-energy threshold,…
Threshold dynamics for the 4 mass-energy double critical NLS
Alex H. Ardila, Zuyu Ma, Jason Murphy +1
We consider the 4 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…
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= 4…
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…
Scattering norm estimate near the threshold for the energy-subcritical NLS
Zuyu Ma
We consider the focusing energy-subcritical Schrödinger equations. In earlier works by Holmer-Roudenko \cite{holmer}, Duyckaerts-Holmer-Roudenko \cite{duyckaerts2}, Akahori-Nawa \c…
Dynamics of subcritical threshold solutions for the 4d energy-critical NLS
Zuyu Ma, Changxing Miao, Jason Murphy +1
We study dynamics of the 4 energy-critical nonlinear Schrödinger equation at the ground state energy. Previously, Duyckaerts and Merle [Geom. Funct. Anal. (2009)] proved that an…
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…
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 -critical nonlinearity and with inverse-square potential(C…