Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

Advances in Nonlinear Analysis

article

Hugo Beirão da Veiga¹  Jiaqi Yang² 

[1] Department of Mathematics, Pisa University;Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences

关键词: Navier-Stokes equations;    Slip boundary conditions;    No flat boundaries;    Two components regularity criterium;   

DOI  :  10.1515/anona-2020-0017

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ 3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case R+3 $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

【 授权许可】

CC BY