SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3306-3337, January 2021.
In this paper, inspired by the seminal work by Caffarelli, Kohn, and Nirenberg [Comm. Pure Appl. Math., 35 (1982), pp. 771--831] on the incompressible Navier--Stokes equation, we establish the existence of a suitable weak solution to the Navier--Stokes--Planck--Nernst--Poisson equation in dimension three, which is smooth away from a closed set whose 1-dimensional parabolic Hausdorff measure is zero.

中文翻译：

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Navier--Stokes--Planck--Nernst--Poisson方程的合适弱解的偏正则性

SIAM 数学分析杂志，第 53 卷，第 3 期，第 3306-3337 页，2021
年1 月。本文的灵感来自 Caffarelli、Kohn 和 Nirenberg 的开创性工作 [Comm. 纯应用 Math., 35 (1982), pp. 771--831] 关于不可压缩的 Navier--Stokes 方程，我们建立了 Navier--Stokes--Planck--Nernst--Poisson 方程的合适弱解的存在性维度三，远离一维抛物线豪斯多夫测度为零的闭集是平滑的。