Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow condition
Vol. 3 (1996), No. 1, Page 73--82.
Morimoto, Hiroko ; Ukai, Seiji
Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow condition
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Abstract:
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={\Vecx∈R2;R1<|\Vecx|<R2}, 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 } Î_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 + Ï_i(θ)\} {\Vec e}_{θ} \ \mbox{ on } \ Î_i,\ i=1, 2, where \varphi_i(θ),Ï_i(θ) are 2 Ï-periodic smooth function of θ, under some additional condition.
Mathematics Subject Classification (1991): 35Q30, 76D05
Mathematical Reviews Number: MR1414620
Received: 1995-02-13
