The 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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
3
号
1
ページ
73 - 82
発行年
1996
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1414620
Mathmatical Subject Classification
76D05(MSC1991)
35Q30(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow condition
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