26 citations · 174 across the 43 of their papers we have counts for
52 papers
Nonradial Finite-Time Blow-up for the Mass-Critical Inhomogeneous Biharmonic NLS
Ngoc Uyen Cong Nguyen, Van Duong Dinh
We consider the focusing mass-critical inhomogeneous biharmonic nonlinear Schrödinger equation \[ i\partial_tu=Δ^2u-|x|^{-b}|u|^{\frac{8-2b}{N}}u, \quad 0<b<\min\{4,N/2\}. \] We pr…
Finite-time blow-up for the four-dimensional mass-critical quadratic nonlinear Schrödinger system without mass resonance
Ngoc Uyen Cong Nguyen, Van Duong Dinh
We study the focusing quadratic nonlinear Schrödinger system \[ \begin{cases} i\partial_t u+Δu=-2v\overline{u}, \\ i\partial_t v+κΔv=-u^2, \end{cases} \qquad (t,x)\in I\times\mathb…
From bosonic canonical ensembles to non-linear Gibbs measures
van Duong Dinh, Nicolas Rougerie
We study the mean-field limit of the 1D bosonic canonical ensemble in a superharmonic trap. This is the regime with temperature proportional to particle number, both diverging to i…
Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps
Van Duong Dinh, Nicolas Rougerie, Leonardo Tolomeo +1
In this paper, we investigate the Gibbs measures associated with the focusing nonlinear Schrödinger equation with an anharmonic potential. We establish a dichotomy for normalizabil…
Invariant Gibbs measures for 1D NLS in a trap
Van Duong Dinh, Nicolas Rougerie
We consider the one dimensional cubic nonlinear Schr{ö}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to th…
Energy scattering for a class of inhomogeneous biharmonic nonlinear Schrödinger equations in low dimensions
Van Duong Dinh, Sahbi Keraani
We consider a class of biharmonic nonlinear Schrödinger equations with a focusing inhomogeneous power-type nonlinearity \[ i\partial_t u -Δ^2 u+μΔu +|x|^{-b} |u|^αu=0, \quad \left.…
A system of inhomogeneous NLS arising in optical media with a nonlinearity, part I : Dynamics
Van Duong Dinh, Amin Esfahani
We study a system of inhomogeneous nonlinear Schrödinger equations that emerge in optical media with a nonlinearity. This nonlinearity, whose local strength is subject to…
Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach
Jacopo Bellazzini, Van Duong Dinh, Luigi Forcella
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlineariti…
Blow-up of 2D attractive Bose-Einstein condensates at the crittical rotational speed
Van Duong Dinh, Dinh-Thi Nguyen, Nicolas Rougerie
We study the ground states of a 2D focusing non-linear Schrödinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value fr…
The 3D nonlinear Schrödinger equation with a constant magnetic field revisited
Van Duong Dinh
In this paper, we revisit the Cauchy problem for the three dimensional nonlinear Schrödinger equation with a constant magnetic field. We first establish sufficient conditions that…
Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed
Van Duong Dinh
We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially…
Long time dynamics and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with spatial growing nonlinearity
Van Duong Dinh, Mohamed Majdoub, Tarek Saanouni
We investigate the Cauchy problem for the focusing inhomogeneous nonlinear Schrödinger equation in the radial Sobolev space $H^1_{\text{…
Long time dynamics of non-radial solutions to inhomogeneous nonlinear Schrödinger equations
Van Duong Dinh, Sahbi Keraani
We study long time dynamics of non-radial solutions to the focusing inhomogeneous nonlinear Schrödinger equation. By using the concentration/compactness and rigidity method, we est…
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with nonlinear response
Alex H. Ardila, Van Duong Dinh, Luigi Forcella
We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold crite…
Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction
Van Duong Dinh, Luigi Forcella
We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetr…
On stability of rotational 2D binary Bose-Einstein condensates
Rémi Carles, Van Duong Dinh, Hichem Hajaiej
We consider a two-dimensional nonlinear Schr{ö}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modificat…
Random data theory for the cubic fourth-order nonlinear Schrödinger equation
Van Duong Dinh
We consider the cubic nonlinear fourth-order Schrödinger equation \[ i\partial_t u - Δ^2 u + μΔu = \pm |u|^2 u, \quad μ\geq 0 \] on with random initial dat…
Mass-Energy threshold dynamics for dipolar Quantum Gases
Van Duong Dinh, Luigi Forcella, Hichem Hajaiej
We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We descri…
Long time dynamics for the focusing nonlinear Schrödinger equation with exponential nonlinearities
Van Duong Dinh, Sahbi Keraani, Mohamed Majdoub
In this paper, we study the focusing nonlinear Schrödinger equation with exponential nonlinearities \[ i \partial_t u + Δu = - \left(e^{4π|u|^2} - 1 - 4πμ|u|^2 \right) u, \quad u(0…
Blow-up criteria for linearly damped nonlinear Schrödinger equations
Van Duong Dinh
We consider the Cauchy problem for linearly damped nonlinear Schrödinger equations \[ i\partial_t u + Δu + i a u= \pm |u|^αu, \quad (t,x) \in [0,\infty) \times \mathbb{R}^N, \] whe…
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations
Van Duong Dinh
We consider the following class of focusing -supercritical fourth-order nonlinear Schrödinger equations \[ i\partial_t u - Δ^2 u + μΔu = - |u|^αu, \quad (t,x) \in \mathbb{R} \…
Non-radial scattering theory for nonlinear Schrödinger equations with potential
Van Duong Dinh
We consider a class of nonlinear Schrödinger equations with potential \[ i\partial_t u +Δu - Vu = \pm |u|^αu, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3, \] where $\frac{4}{3}<…
Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials
Van Duong Dinh
We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional nonlinear Schrödinger equation with periodic potentials. Usin…
Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions
Van Duong Dinh
We consider a class of -supercritical inhomogeneous nonlinear Schrödinger equations in two dimensions \[ i\partial_t u + Δu = \pm |x|^{-b} |u|^αu, \quad (t,x) \in \mathbb{R} \…