25 citations · 25 across the 9 of their papers we have counts for
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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…
Dynamics of the Energy-Critical Nonlinear Schrödinger System in
Alex H. Ardila
In this paper, we investigate the dynamics of radial solutions at threshold energy for a 3-component Schrödinger system with cubic nonlinearity in four dimensions. The main differe…
Threshold solutions for the energy-critical NLS system with quadratic interaction
Alex H. Ardila, Liliana Cely, Fanfei Meng
In this paper, we study the Cauchy problem for a quadratic nonlinear Schrödinger system in dimension six. In~\cite{GaoMengXuZheng}, the authors classified the behavior of solutions…
Threshold dynamics for the 3 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…
Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential
Alex H. Ardila, Masaru Hamano, Masahiro Ikeda
In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exac…