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Kinetic and Related Models (KRM)
 

Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction

Pages: 165 - 191, Volume 9, Issue 1, March 2016      doi:10.3934/krm.2016.9.165

 
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Xueke Pu - Department of Mathematics, Chongqing University, Chongqing 401331, China (email)
Boling Guo - Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China (email)

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:  Quantum hydrodynamics, global solutions, semiclassical limit.
Mathematics Subject Classification:  Primary: 35M20; Secondary: 35Q35.

Received: June 2015;      Revised: September 2015;      Available Online: October 2015.

 References