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math.AP2026
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,…
math.AP2024
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…