应用数学学报
首页  |  期刊介绍  |  编 委 会  |  投稿指南  |  期刊订阅  |  广告服务  |  相关链接  |  下载中心  |  联系我们  |  留言板
 
应用数学学报 英文版  
   
   
高级检索 »  
应用数学学报  2014, Vol. 37 Issue (2): 265-277    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索  |   
Navier-Stokes-Nernst-Planck-Poisson系统弱解的时间衰减率
张兴伟
首都师范大学数学科学学院, 北京 100048
The Time Decay Rates of the Weak Solutions to Navier-Stokes-Nernst-Planck-Poisson System
ZHANG Xingwei
Department of Mathematical Sciences, Capital Normal University, Beijing 100048
 全文: PDF (312 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文主要研究了一类描述电流体动力学行为的 耦合型Navier-Stokes-Nernst-Planck-Poisson系统的Cauchy问题. 对二维任意的大初值和三维小初值得到了系统强解的整体存在性,以及三维空间弱解的大时间衰减率.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
张兴伟
关键词Navier-Stokes方程   Nernst-Planck-Poisson   衰减率     
Abstract: We consider the Cauchy problem of a coupled Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electro-hydrodynamics, and show the global existence of unique strong solution in 2D for general large initial data and in 3D for small initial data. The time decay rates of the weak solutions in 3D is also obtained.
Key wordsNavier-Stokes equations   Nernst-Planck-Poisson   decay rates   
收稿日期: 2013-10-07;
基金资助:国家自然科学基金(11171228,11231006,11225102)和北京市属高等学校 高层次人才引进与培养计划(20140323)资助项目.
引用本文:   
张兴伟. Navier-Stokes-Nernst-Planck-Poisson系统弱解的时间衰减率[J]. 应用数学学报, 2014, 37(2): 265-277.
ZHANG Xingwei. The Time Decay Rates of the Weak Solutions to Navier-Stokes-Nernst-Planck-Poisson System[J]. Acta Mathematicae Applicatae Sinica, 2014, 37(2): 265-277.
 
[1] Rubinstein I. Electro-diffusion of Ions. Philadelphia: SIAM, 1990
[2] Leray J. Sur le Mouvement dun Kiquide Visqueux Emplissant Lespace. Acta Math., 1934, 63: 193-248
[3] Hopf E. Uber die Anfangswertaufgabe f黵 die Hydrodynamischen Grundgleichungen. Math. Nachr., 1951, 4: 213-231
[4] Dong B Q. Time Decay Rates of the Isotropic Non-Newtonian Flows in Rn. Acta Math. Appl. Sinica (English Series), 2007, 23(1): 99-106
[5] He C, Xin Z. On the Decay Properties of Solutions to the Non-stationary Navier-Stokes Equations in R3. Proc. Roy. Soc. Edinburgh Sect. A., 2001, 131(3): 597-619
[6] Heywood J G. The Navier-Stokes Equations: on the Existence, Regularity and Decay of Solutions. Indiana Univ. Math. J., 1980, 29: 639-681
[7] Kato T. Strong LP Solutions of the Navier-Stokes Equations in Rm with Applications to Weak Solutions. Math. Z., 1984, 187: 471-480
[8] Schonbek M E. L2 Decay for Weak Solutions of the Navier-Stokes Equations. Arch. Rational Mech. Anal., 1985, 88: 209-222
[9] Schonbek M E. Large Time Behaviour of Solutions to the Navier-Stokes Equations. Commun. Part. Diff. Eqns., 1986, 11: 733-763
[10] Kurokiba M, Ogawa T. Well-posedness for the Drift-diffusion System in LP Arising from the Semiconductor Device Simulation. J. Math. Anal. Appl., 2008, 342: 1052-1067
[11] Kawashima S, Nishibata S, Nishikawa M. LP Energy Method for Multi-dimensional Viscous Conservation Laws and Application to the Stability of Planar Waves. J. Hyperbolic Differ. Equ., 2004, 3: 581-603
[12] Kobayashi R, Kawashima S. Decay Estimates and Large Time Behavior of Solutions to the drift-diffusion System. Funkcialaj Ekvacioj, 2008, 51: 371-394
[13] Schmuck M. Analysis of the Navier-Stokes-Nernst-Planck-Poisson System. Math. Mod. Meth. Appl. Sci., 2009, 19(6): 993-1015
[14] Ryham R J. Existence, Uniqueness, Regularity and Long-term Behavior for Dissipative Systems Modeling Electrohydrodynamics. arXiv: 0910.4973v1
[15] Jerome J W. An Analytical Approach to Charge Transport in a Moving Medium. Trans. Theory Statist. Phys., 2002, 31: 333-366
[16] Zhao J, Deng C, Cui S. Well-posedness of a Dissipative System Modeling Electrohydrodynamics in Lebesgue Spaces, Diff. Eqns. & Appl., 2011, 3(3): 427-448
[17] Stein E. Singular Integrals and Differentiability Properties of Functions. Princeton, NJ: Princeton Univ. Press, 1970
[18] Ladyzhenskaya O A. The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon Breach, 1969
[19] Temam R. Navier-Stokes Equations, Theory and Numerical Analysis. Amsterdam: North-Holland, 1977
[1] 李开泰, 于佳平, 刘德民. 复杂边界旋转Navier-Stokes方程的几何方法及二度并行算法[J]. 应用数学学报, 2012, (1): 1-41.
[2] 王立周. 求解Navier-Stokes方程的非退化转向点的扩充系统的一步牛顿迭代法[J]. 应用数学学报, 2002, 25(3): 0-0.
[3] 赵春山, 李开泰. 二维全空间上线性阻尼Navier-Stokes方程的全局吸引子及其维数估计[J]. 应用数学学报, 2000, 23(1): 90-098.
[4] 施小丁. 一类修正的Navier-Stokes方程组Neumann边值问题的弱解[J]. 应用数学学报, 1998, 21(4): 0-0.
[5] 吴珞. Navier-Stokes方程的稳态解和吸引子[J]. 应用数学学报, 1998, 21(3): 0-0.
[6] 张兴伟. Navier-Stokes-Nernst-Planck-Poisson系统弱解的时间衰减率[J]. 应用数学学报, 0, (): 265-277.
  版权所有 © 2009 应用数学学报编辑部   E-mail: amas@amt.ac.cn
京ICP备05002806号-9