Tuan Tran

collaborators

3 papers

math.FA2026

Semiclassical Moser--Trudinger type inequalities for orthonormal families in $R^{2}$

Phuoc-Tai Nguyen, Tuan-Dat Tran

For $H^{1} (R^{2})$ -orthonormal families ${u_{n}}_{n = 1}^{N}$ with one-body density $ρ = \sum_{n = 1}^{N} ∣ u_{n} ∣^{2}$ , we prove the whole-space endpoint Moser--Trudinger inequality $$ \int…

math.AP2026

Nonlinear Schrödinger equations with critical Hardy potential and Choquard nonlinearity

Phuoc-Tai Nguyen, Tuan Dat Tran

We study the Cauchy problem for the nonlinear Schrödinger equation characterized by contrasting effects between the concentration at the origin of a critical Hardy potential and th…

math.CO2023

Variants of VC dimension and their applications to dynamics

Guorong Gao, Jie Ma, Mingyuan Rong +1

Since its introduction by Vapnik and Chervonenkis in the 1960s, the VC dimension and its variants have played a central role in numerous fields. In this paper, we investigate sever…

Semiclassical Moser--Trudinger type inequalities for orthonormal families in R2

Nonlinear Schrödinger equations with critical Hardy potential and Choquard nonlinearity

Variants of VC dimension and their applications to dynamics

Semiclassical Moser--Trudinger type inequalities for orthonormal families in $R^{2}$