THE VISCOUS MODEL OF QUANTUM HYDRODYNAMICS IN SEVERAL DIMENSIONS-Reference-Cited by-同舟云学术

THE VISCOUS MODEL OF QUANTUM HYDRODYNAMICS IN SEVERAL DIMENSIONS

Published:2007-07 Issue:07 Volume:17 Page:1065-1093
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

CHEN LI¹,DREHER MICHAEL²

Affiliation:

1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China

2. Fachbereich Mathematik und Statistik, P. O. Box D187, Universität Konstanz, 78457 Konstanz, Germany

Abstract

We investigate the viscous model of quantum hydrodynamics in one and higher space dimensions. Exploiting the entropy dissipation method, we prove the exponential decay to the thermal equilibrium state in one, two, and three dimensions, provided that the domain is a box. Further, we show the local in time existence of a solution in the one-dimensional case; and in the case of higher dimensions under the assumption of periodic boundary conditions. Finally, we prove the global existence in a one-dimensional setting under additional assumptions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202507002200

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