2020-08-04T04:30:09Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000403312020-07-10T06:57:17Z00312:06865:07055:0706100009:00504:06868:07057:07062
Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow conditionenghttp://hdl.handle.net/2261/1546Departmental Bulletin PaperMorimoto, HirokoThe boundary value problem of the Navier-Stokes equations has been studied so far only under the vanishing outflow condition due to Leray. We consider this problem in an annular domain $ D = \{ {\Vec x} \in {\bf R}^2 ; R_1 < |{\Vec x}| < R_2 \},$ under the boundary condition with non-vanishing outflow. In a previous paper of the first author, an exact solution is obtained for a simple boundary condition of non-vanishing outflow type: ${\Vec u} = \displaystyle{μ \over R_i} {\Vec e}_r + b_i{\Vec e}_θ \ \mbox{ on } Γ_i, \ i=1, 2, $ where $μ,b_1,b_2$ are arbitrary constants. In this paper, we show the existence of solutions satisfying the boundary condition: $ {\Vec u} = \{ \displaystyle{μ \over {R_i}}+ \varphi_i(θ)\}{\Vec e}_r + \{b_i + ψ_i(θ)\} {\Vec e}_{θ} \ \mbox{ on } \ Γ_i,\ i=1, 2, $ where $\varphi_i(θ),ψ_i(θ)$ are $2 π$-periodic smooth function of $θ$, under some additional condition.Journal of mathematical sciences, the University of Tokyo317382199613405705AA11021653application/pdf415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40331&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14