Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation

Huajun Gong; Changyou Wang; Xiaotao Zhang

Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation

Analysis of PDEs 2019-06-18 v2

Authors: Huajun Gong , Changyou Wang , Xiaotao Zhang

Abstract

In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg \cite{CKN} 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 shown to be smooth away from a closed set whose $1$ -dimensional parabolic Hausdorff measure is zero.

Keywords

navier-stokes-planck-nernst-poisson equation suitable weak solution partial regularity parabolic hausdorff measure existence theorem

Cite

@article{arxiv.1905.13365,
  title  = {Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation},
  author = {Huajun Gong and Changyou Wang and Xiaotao Zhang},
  journal= {arXiv preprint arXiv:1905.13365},
  year   = {2019}
}

Comments

31 pages. A few mistakes have been fixed

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