## International Journal of Differential Equations

### Global Existence and Asymptotic Behavior of Self-Similar Solutions for the Navier-Stokes-Nernst-Planck-Poisson System in ${\Bbb R}^{3}$

#### 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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 329014, 19 pages.

Dates
Accepted: 5 September 2011
First available in Project Euclid: 25 January 2017

https://projecteuclid.org/euclid.ijde/1485313251

Digital Object Identifier
doi:10.1155/2011/329014

Mathematical Reviews number (MathSciNet)
MR2847600

Zentralblatt MATH identifier
1234.35204

#### Citation

Zhao, Jihong; Deng, Chao; Cui, Shangbin. Global Existence and Asymptotic Behavior of Self-Similar Solutions for the Navier-Stokes-Nernst-Planck-Poisson System in ${\Bbb R}^{3}$. Int. J. Differ. Equ. 2011 (2011), Article ID 329014, 19 pages. doi:10.1155/2011/329014. https://projecteuclid.org/euclid.ijde/1485313251

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