Abstract and Applied Analysis
Volume 2012 (2012), Article ID 864186, 14 pages
http://dx.doi.org/10.1155/2012/864186
Research Article

Uniqueness of Weak Solutions to an Electrohydrodynamics Model

Yong Zhou1 and Jishan Fan2

1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China

Received 11 October 2011; Accepted 3 March 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2012 Yong Zhou and Jishan Fan. 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

This paper studies uniqueness of weak solutions to an electrohydrodynamics model in ℝ 𝑑 ( 𝑑 = 2 , 3 ) . When 𝑑 = 2 , we prove a uniqueness without any condition on the velocity. For 𝑑 = 3 , we prove a weak-strong uniqueness result with a condition on the vorticity in the homogeneous Besov space.