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Zbl 1181.35170
Fan, Jishan; Gao, Hongjun
Uniqueness of weak solutions to a model of electro-kinetic fluid. (English)
[J] Commun. Math. Sci. 7, No. 2, 411-421 (2009). ISSN 1539-6746

Summary: 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 [{\it P. Biler, W. Hebisch} and {\it T. Nadzieja}, Nonlinear Anal., Theory Methods Appl. 23, No.~9, 1189--1209 (1994; Zbl 0814.35054); {\it R. Ryham, C. Liu} and {\it Z.-Q. Wang}, Mathematical modelling for electro-kinetic fluids: analysis and simulation, Preprint (2005), {\it R. Ryham}, Global existence and long term behavior of 2D electro-hydrodynamics, arXiv:0810.2064].

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
35D30
76W05 Flows in presence of electromagnetic forces

Citations: Zbl 0814.35054

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