Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction
Mathematical Physics
2016-07-27 v1 Analysis of PDEs
math.MP
Abstract
The hydrodynamic equations with quantum effects are studied in this paper. First we establish the global existence of smooth solutions with small initial data and then in the second part, we establish the convergence of the solutions of the quantum hydrodynamic equations to those of the classical hydrodynamic equations. The energy equation is considered in this paper, which added new difficulties to the energy estimates, especially to the selection of the appropriate Sobolev spaces.
Keywords
Cite
@article{arxiv.1504.05304,
title = {Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction},
author = {Xueke Pu and Boling Guo},
journal= {arXiv preprint arXiv:1504.05304},
year = {2016}
}