6 papers
Instability of gray solitons in a Gross-Pitaevskii model with a moving impurity
Paolo Antonelli, Martino Caliaro
The effect of a moving impurity in a dilute Bose-Einstein condensate is investigated by means of the one-dimensional Gross-Pitaevskii model (GP) with non-zero boundary conditions a…
On the Gross-Pitaevskii model with a moving impurity: Cauchy problem and superfluidity criterion
Paolo Antonelli, Martino Caliaro
We study the one-dimensional Gross-Pitaevskii equation with a traveling delta potential and non-zero conditions at infinity. This model describes the effect of a moving impurity in…
Initial layer analysis of relaxation-time limit of the collisional QHD
Paolo Antonelli, Pierangelo Marcati, Hao Zheng
We study the structure of the initial layer arising in the relaxation-time limit of the collisional quantum hydrodynamic (QHD) system. When the initial data are not well prepared,…
The time-relaxation limit for weak solutions to the quantum hydrodynamics system
Paolo Antonelli, Pierangelo Marcati, Hao Zheng
This paper analyzes weak solutions of the quantum hydrodynamics (QHD) system with a collisional term posed on the one-dimensional torus. The main goal of our analysis is to rigorou…
Finite energy well-posedness for nonlinear Schrödinger equations with non-vanishing conditions at infinity
Paolo Antonelli, Lars Eric Hientzsch, Pierangelo Marcati
Relevant physical phenomena are described by nonlinear Schrödinger equations with non-vanishing conditions at infinity. This paper investigates the respective 2D and 3D Cauchy pro…
An intrinsically hydrodynamic approach to multidimensional QHD systems
Paolo Antonelli, Pierangelo Marcati, Hao Zheng
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis init…