Global axisymmetric solutions to the 3D Navier--Stokes--Poisson--Nernst--Planck system in the exterior of a cylinder
Bull. Korean Math. Soc. 2021 Vol. 58, No. 3, 729-744
https://doi.org/10.4134/BKMS.b200536
Published online May 10, 2021
Printed May 31, 2021
Jihong Zhao
Baoji University of Arts and Sciences
Abstract : In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodyna\-mic 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 $L^{p}$ 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
MSC numbers : Primary 35B07, 35D35, 35K55, 76W05
Supported by : This work was financially supported by the National Natural Science Foundation of China (no. 11961030) and the Natural Science Foundation of Shaanxi Province (no. 2018JM1004)
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