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On the Nernst–Planck–Navier–Stokes system

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Abstract

We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier–Stokes and Poisson equations, and blocking (vanishing normal flux) or selective (Dirichlet) boundary conditions for the ionic concentrations. We prove global existence and stability results for large data.

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Acknowledgements

We would like to thank the referee for helpful suggestions to improve the presentation. The work of PC was partially supported by NSF Grant DMS-1713985.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Peter Constantin & Mihaela Ignatova

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  1. Peter Constantin
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  2. Mihaela Ignatova
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Correspondence to Peter Constantin.

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Communicated by V. Šverák

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Constantin, P., Ignatova, M. On the Nernst–Planck–Navier–Stokes system. Arch Rational Mech Anal 232, 1379–1428 (2019). https://doi.org/10.1007/s00205-018-01345-6

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  • DOI: https://doi.org/10.1007/s00205-018-01345-6

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