کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4613881 | 1339274 | 2016 | 23 صفحه PDF | دانلود رایگان |

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∈R+t∈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 close 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.
Journal: Journal of Mathematical Analysis and Applications - Volume 444, Issue 1, 1 December 2016, Pages 275–297