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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
Global Uniqueness of Subsonic Flows for the Steady Euler-Poisson System
Myoungjean Bae, Ben Duan, Chunjing Xie
We prove the global uniqueness of multidimensional subsonic flows for the steady Euler--Poisson system in a bounded nozzle in the sense that uniqueness holds without restricting so…
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…