Global solutions for the compressible quantum hydrodynamic model in a bounded domain

被引:4
作者
Pu, Xueke [1 ]
Li, Min [2 ]
机构
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
[2] Shanxi Univ Finance & Econ, Fac Appl Math, Taiyuan 030006, Shanxi, Peoples R China
关键词
Full quantum hydrodynamic model; Initial boundary value problem; Global smooth solutions; Energy estimates; STABILITY; EQUATIONS; LIMIT;
D O I
10.1016/j.na.2019.01.029
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper concerns the existence of global smooth solutions to the initial boundary value problem for a three-dimensional compressible quantum hydrodynamic model with damping and heat diffusion in a bounded domain in R-3. Based on the continuation argument and the uniform a priori estimates with respect to the time, we obtain the existence of global solutions in a bounded smooth domain provided that the initial perturbation around a constant state is small enough. The key difficulty is to deal with the higher order quantum terms, which do play an essential role in establishing the a priori estimates. The boundary conditions finally adopted are the insulating boundary conditions. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码:148 / 171
页数:24
相关论文
共 33 条
[21]   QUASINEUTRAL LIMIT FOR THE QUANTUM NAVIER-STOKES-POISSON EQUATIONS [J].
Li, Min ;
Pu, Xueke ;
Wang, Shu .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2017, 16 (01) :273-293
[22]   Steady-state solutions and asymptotic limits on the multi-dimensional semiconductor quantum hydrodynamic model [J].
Liang, Bo ;
Zhang, Kaijun .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (02) :253-275
[23]  
Madelung E, 1926, Z PHYS, V40, P322
[24]   Initial boundary value problems for a quantum hydrodynamic model of semiconductors: Asymptotic behaviors and classical limits [J].
Nishibata, Shinya ;
Suzuki, Masahiro .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (04) :836-874
[25]   Asymptotic Stability of a Stationary Solution to a Thermal Hydrodynamic Model for Semiconductors [J].
Nishibata, Shinya ;
Suzuki, Masahiro .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 192 (02) :187-215
[27]   GLOBAL EXISTENCE AND SEMICLASSICAL LIMIT FOR QUANTUM HYDRODYNAMIC EQUATIONS WITH VISCOSITY AND HEAT CONDUCTION [J].
Pu, Xueke ;
Guo, Boling .
KINETIC AND RELATED MODELS, 2016, 9 (01) :165-191
[28]   On the quantum correction for thermodynamic equilibrium [J].
Wigner, E .
PHYSICAL REVIEW, 1932, 40 (05) :0749-0759
[29]  
2002, MATH MODELS METHODS, V12, P485
[30]  
2004, Q APPL MATH, V62, P569