Bulletin of the
Korean Mathematical Society BKMS

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)