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| 量子Navier-Stokes方程组的热平衡解 | |
| 引用本文： | 董建伟. 量子Navier-Stokes方程组的热平衡解[J]. 阜阳师范学院学报(自然科学版), 2012, 29(2): 14-16 |
| 作者姓名： | 董建伟 |
| 作者单位： | 郑州航空工业管理学院数理系,河南郑州,450015 |
| 基金项目： | 河南省高等学校青年骨干教师资助计划项目，河南省教育厅科学技术研究重点项目 |
| 摘 要： | 在Dirichlet-Neumann混合边界条件下研究量子Navier-Stokes方程组的热平衡状态.首先利用截断方法把问题正则化,然后利用Leray-Schauder不动点定理证明正则化问题解的存在性,最后通过寻找粒子浓度的一个正则性估计证明正则化问题的解也是原问题的解,另外证明问题解的唯一性。 |
| 关 键 词： | 量子Navier-Stokes方程组 热平衡 混合边值问题 存在性 唯一性 |
Thermal equilibrium solution of quantum Navier-Stokes equations |
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| DONG Jian-wei. Thermal equilibrium solution of quantum Navier-Stokes equations[J]. Journal of Fuyang Teachers College:Natural Science, 2012, 29(2): 14-16 | |
| Authors: | DONG Jian-wei |
| Affiliation: | DONG Jian-wei(Department of Mathematics and Physics,Zhengzhou Institute of Aeronautical Industry Management,Zhengzhou Henan 450015,China) |
| Abstract: | The thermal equilibrium state of the quantum Navier-Stokes equations under the Dirichlet-Neumann mixed boundary conditions is studied.First,the problem is regularized by using the truncation method.Next,the existence of the solution of the regularized problem is proved by the Leray-Schauder fixed point theorem.Finally,it is shown that the solution of the regularized problem is also solution to the original problem,by finding a regularized estimate for the particle density.In addition,the uniqueness of the solution is shown. |
| Keywords: | quantum Navier-Stokes equations thermal equilibrium mixed boundary value problem existence uniqueness |
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