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math.AP2026
Global Existence of Classical Solutions to the Relativistic Quantum Hydrodynamic System with Small Initial Data
Ben Duan, Rongrong Yan
We establish global existence, decay, and scattering for sufficiently small, smooth, and localized perturbations of a constant non-vacuum equilibrium of a relativistic quantum hydr…
math.AP2026
Derivation and local well-posedness of a relativistic quantum hydrodynamic system on the Heisenberg group
Ben Duan, Yutian Li, Rongrong Yan +1
We derive and analyze a relativistic quantum hydrodynamic (RQHD) system on the Heisenberg group. Starting from the Klein--Gordon--Poisson system, we apply the Madelung transformati…
math.AP2025
A relativistic quantum Euler-Poisson system derived from the Klein-Gordon-Poisson equation: hyperbolic-elliptic structure
Ben Duan, Jun Li, Bin Guo +1
In the Klein-Gordon equation, quantum and relativistic parameters are strongly coupled, which poses significant analytical challenges in the derivation and analysis of related clas…