International Journal of Differential Equations
Volume 2011 (2011), Article ID 329014, 19 pages
http://dx.doi.org/10.1155/2011/329014
Research Article

Global Existence and Asymptotic Behavior of Self-Similar Solutions for the Navier-Stokes-Nernst-Planck-Poisson System in ℝ 3

Jihong Zhao,1 Chao Deng,2 and Shangbin Cui3

1Institute of Applied Mathematics, College of Science, Northwest A&F University, Shaanxi, Yangling 712100, China
2Department of Mathematics, Xuzhou Normal University, Jiangsu, Xuzhou 221009, China
3Department of Mathematics, Sun Yat-sen University, Guangdong, Guangzhou 510275, China

Received 5 May 2011; Accepted 5 September 2011

Academic Editor: Chérif Amrouche

Copyright © 2011 Jihong Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electrohydrodynamics. For small initial data, the global existence, uniqueness, and asymptotic stability as time goes to infinity of self-similar solutions to the Cauchy problem of this system posed in the whole three dimensional space are proved in the function spaces of pseudomeasure type.