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http://dx.doi.org/10.4134/BKMS.b200536

GLOBAL AXISYMMETRIC SOLUTIONS TO THE 3D NAVIER-STOKES-POISSON-NERNST-PLANCK SYSTEM IN THE EXTERIOR OF A CYLINDER  

Zhao, Jihong (School of Mathematics and Information Science Baoji University of Arts and Sciences)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.3, 2021 , pp. 729-744 More about this Journal
Abstract
In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodynamic model based on the coupled Navier-Stokes-Poisson-Nernst-Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the Lp interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.
Keywords
Navier-Stokes-Poisson-Nernst-Planck equations; axisymmetric solutions; global existence;
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1 J. W. Jerome and R. Sacco, Global weak solutions for an incompressible charged fluid with multi-scale couplings: initial-boundary-value problem, Nonlinear Anal. 71 (2009), no. 12, e2487-e2497. https://doi.org/10.1016/j.na.2009.05.047   DOI
2 K. Abe and G. Seregin, Axisymmetric flows in the exterior of a cylinder, Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), no. 4, 1671-1698. https://doi.org/10.1017/prm.2018.121   DOI
3 H. Abidi, Resultats de regularite de solutions axisymetriques pour le systeme de NavierStokes, Bull. Sci. Math. 132 (2008), no. 7, 592-624. https://doi.org/10.1016/j.bulsci.2007.10.001   DOI
4 O. A. Ladyzenskaja, Unique global solvability of the three-dimensional Cauchy problem for the Navier-Stokes equations in the presence of axial symmetry, Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 (1968), 155-177.
5 J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934), no. 1, 193-248. https://doi.org/10.1007/BF02547354   DOI
6 I. Rubinstein, Electro-diffusion of ions, SIAM Studies in Applied Mathematics, 11, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. https://doi.org/10.1137/1.9781611970814
7 R. J. Ryham, Existence, uniqueness, regularity and long-term behavior for dissipative systems modeling electrohydrodynamics, arXiv:0910.4973v1.
8 M. Schmuck, Analysis of the Navier-Stokes-Nernst-Planck-Poisson system, Math. Models Methods Appl. Sci. 19 (2009), no. 6, 993-1015. https://doi.org/10.1142/S0218202509003693   DOI
9 M. R. Ukhovskii and V. I. Iudovich, Axially symmetric flows of ideal and viscous fluids filling the whole space, J. Appl. Math. Mech. 32 (1968), 52-61. https://doi.org/10.1016/0021-8928(68)90147-0   DOI
10 J. Zhao and Q. Liu, Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces, J. Differential Equations 263 (2017), no. 2, 1293-1322. https://doi.org/10.1016/j.jde.2017.03.015   DOI
11 J. Zhao, T. Zhang, and Q. Liu, Global well-posedness for the dissipative system modeling electro-hydrodynamics with large vertical velocity component in critical Besov space, Discrete Contin. Dyn. Syst. 35 (2015), no. 1, 555-582. https://doi.org/10.3934/dcds.2015.35.555   DOI
12 S. Leonardi, J. Malek, J. Necas, and M. Pokorny, On axially symmetric flows in R3, Z. Anal. Anwendungen 18 (1999), no. 3, 639-649. https://doi.org/10.4171/ZAA/903   DOI
13 J. Zhao, C. Deng, and S. Cui, Well-posedness of a dissipative system modeling electrohydrodynamics in Lebesgue spaces, Differ. Equ. Appl. 3 (2011), no. 3, 427-448. https://doi.org/10.7153/dea-03-27   DOI
14 H. Ma, Global large solutions to the Navier-Stokes-Nernst-Planck-Poisson equations, Acta Appl. Math. 157 (2018), 129-140. https://doi.org/10.1007/s10440-018-0167-0   DOI
15 J. W. Jerome, The steady boundary value problem for charged incompressible fluids: PNP/Navier-Stokes systems, Nonlinear Anal. 74 (2011), no. 18, 7486-7498. https://doi.org/10.1016/j.na.2011.08.003   DOI
16 J. Fan, F. Li, and G. Nakamura, Regularity criteria for a mathematical model for the deformation of electrolyte droplets, Appl. Math. Lett. 26 (2013), no. 4, 494-499. https://doi.org/10.1016/j.aml.2012.12.003   DOI
17 J. Fan, G. Nakamura, and Y. Zhou, On the Cauchy problem for a model of electrokinetic fluid, Appl. Math. Lett. 25 (2012), no. 1, 33-37. https://doi.org/10.1016/j.aml.2011.07.004   DOI
18 E. Hopf, Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen, Math. Nachr. 4 (1951), 213-231. https://doi.org/10.1002/mana.3210040121   DOI
19 O. A. Ladyzenskaja, The mathematical theory of viscous incompressible flow, Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu. Mathematics and its Applications, Vol. 2, Gordon and Breach, Science Publishers, New York, 1969.
20 J. W. Jerome, Analytical approaches to charge transport in a moving medium, Transport Theory Statist. Phys. 31 (2002), no. 4-6, 333-366. https://doi.org/10.1081/TT120015505   DOI