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Uniqueness of weak solutions to a model of electro-kinetic fluid. (English) Zbl 1181.35170

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

MSC:

35Q30 Navier-Stokes equations
35D30 Weak solutions to PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics

Citations:

Zbl 0814.35054
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