Stability of two-dimensional solutions to the Navier-Stokes equations in cylindrical domains under Navier boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Zajaczkowski, W. M.^1,2 

[1] Polish Acad Sci, Inst Math, Sniadeckich 8, PL-00656 Warsaw, Poland

[2] Mil Univ Technol, Cybernet Fac, Inst Math & Cryptol, Kaliskiego 2, PL-00908 Warsaw, Poland

关键词: Incompressible Navier-Stokes equations;    Stability of two-dimensional solutions;    Global regular solutions;    Navier boundary conditions;   

DOI  :  10.1016/j.jmaa.2016.05.059

来源: Elsevier

【 摘 要 】

The Navier-Stokes motions in a cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that norms bounded with respect to time are controlled by the same constant for all t is an element of R+. Assuming that the initial velocity and the external force are sufficiently close to the initial velocity and the external force of a two-dimensional solution, we prove existence of global three-dimensional solutions which remain dose to the two-dimensional solution for all time. In this sense we have stability of two-dimensional solutions. Thanks to the Navier boundary conditions the nonlinear term in the two-dimensional Navier Stokes equations does not influence the energy estimate. This implies that the global two-dimensional solution is proved without any structural restrictions on the external force, initial data or viscosity. (C) 2016 Published by Elsevier Inc.

【 授权许可】

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