Boundary $\varepsilon$-regularity criteria for the 3D Navier-Stokes equations

Hongjie Dong; Kunrui Wang

Boundary $\varepsilon$-regularity criteria for the 3D Navier-Stokes equations

Analysis of PDEs 2018-12-27 v1

Authors: Hongjie Dong , Kunrui Wang

Abstract

We establish several boundary $\varepsilon$ -regularity criteria for suitable weak solutions for the 3D incompressible Navier-Stokes equations in a half cylinder with the Dirichlet boundary condition on the flat boundary. Our proofs are based on delicate iteration arguments and interpolation techniques. These results extend and provide alternative proofs for the earlier interior results by Vasseur [18], Choi-Vasseur [2], and Phuc-Guevara [6].

Keywords

navier-stokes equations boundary regularity epsilon-regularity weak solutions dirichlet boundary half cylinder

Cite

@article{arxiv.1812.09973,
  title  = {Boundary $\varepsilon$-regularity criteria for the 3D Navier-Stokes equations},
  author = {Hongjie Dong and Kunrui Wang},
  journal= {arXiv preprint arXiv:1812.09973},
  year   = {2018}
}

Comments

18 pages, submitted

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