Local Existence of Solutions to the Transient Quantum Hydrodynamic Equations

JUNGEL, M. C. MARIANI, D. RIAL

MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES

Año: 2002 vol. 12 p. 485 - 495

0218-2025

The existence of weak solutions locally in time to the quantum hiydrodynamic equations in bounded domains is shown. This Madelung-type equations consist of the Euler equations, including the quantum Bohrn potential term, for the particle density and the particle current density and are coupled to the Poisson equation for the electrostatic potential. This model has been used in the modeling of quantum semiconductors and superfluids. The proof of existence results is based on a formulation of the problem as a nonlinear Schoedringer-Poisson system and uses semigroup theory and fixed-points techniques