TY - JOUR

T1 - Nernst–Planck–Navier–Stokes Systems far from Equilibrium

AU - Constantin, Peter

AU - Ignatova, Mihaela

AU - Lee, Fizay Noah

N1 - Funding Information:
The work of PC was partially supported by NSF Grant DMS- 171398. We thank the anonymous referees for useful questions and suggestions.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.

PY - 2021/5

Y1 - 2021/5

N2 - We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data in bounded domains with a smooth boundary in three space dimensions, in the following situations. We consider: a arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. Global regularity holds for any positive, possibly different diffusivities of the ions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier–Stokes coupling, if the velocity is regular. The same global smoothness of solutions is proved to hold for arbitrarily many ionic species as well, but in that case we require all their diffusivities to be the same.

AB - We consider ionic electrodiffusion in fluids, described by the Nernst–Planck–Navier–Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data in bounded domains with a smooth boundary in three space dimensions, in the following situations. We consider: a arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. Global regularity holds for any positive, possibly different diffusivities of the ions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier–Stokes coupling, if the velocity is regular. The same global smoothness of solutions is proved to hold for arbitrarily many ionic species as well, but in that case we require all their diffusivities to be the same.

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U2 - 10.1007/s00205-021-01630-x

DO - 10.1007/s00205-021-01630-x

M3 - Article

AN - SCOPUS:85102362719

SN - 0003-9527

VL - 240

SP - 1147

EP - 1168

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -