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Global regularity criterion for the dissipative systems modelling electrohydrodynamics involving the middle eigenvalue of the strain tensor

Part of: Incompressible viscous fluids Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  21 September 2021

Fan Wu
Fan Wu*
Affiliation:
Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P.R. China ([email protected], [email protected])
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Abstract

In this paper, we study a dissipative systems modelling electrohydrodynamics in incompressible viscous fluids. The system consists of the Navier–Stokes equations coupled with a classical Poisson–Nernst–Planck equations. In the three-dimensional case, we establish a global regularity criteria in terms of the middle eigenvalue of the strain tensor in the framework of the anisotropic Lorentz spaces for local smooth solution. The proof relies on the identity for entropy growth introduced by Miller in the Arch. Ration. Mech. Anal. [16].

Keywords

Navier–Stokes/Poisson–Nernst–Planck systemglobal regularity criteriaanisotropic Lorentz spaces

MSC classification

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 76D03: Existence, uniqueness, and regularity theory 35B65: Smoothness and regularity of solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1277 - 1290
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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