Uniqueness of weak solutions to a model of electro-kinetic fluid

In this paper we prove the uniqueness of weak solutions to a model of electro-kinetic fluid which consists of a momentum equation together with transport equations of charges. Our result is new in that it holds even when the momentum vanishes. The existence of weak solutions has been proved in P.Biler, W. Hebisch and T. Nadzieja, Nonlinear Anal. TMA, 23, 1189-1209, 1994, R. Ryham, C. Liu and Z-Q. Wang, Preprint, 2005, R. Ryham, arXiv: 0810.2064 v1 (math.AP) 12, Oct 2008.

Keywords

Uniqueness, weak solution, electro-kinetic fluid

2010 Mathematics Subject Classification

35Q30

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Published 1 January 2009