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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Mathematical Sciences. The University of Tokyo
( Vol. 3 NO.1 / (1996))
Perturbation of the Navier-Stokes Flow in an Annular Domain with the Non-vanishing Outflow Condition
Hiroko Morimoto, Seiji Ukai,
Pages. 73-82
Abstract The boundary value problem of the Navier-Stokes equations has been studied so far only under the vanishings outflow condition due to Leray. We consider this
problem in an annular domain $D= { x in mathbf R^2 ; R_1 <|x|< R_2 }$, 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: $mathbf u= frac{mu}{R_i} e_r + b_i e_{theta}$ on
$Gamma_i, ; i=1,2,$ where $mu, b_1, b_2$ are arbitrary constants. In this
paper, we show the existence of solutions satisfying the boundary condition:
$mathbf u= { frac{mu}{R_i} + varphi_i (theta) } e_r + {b_i + psi_i
(theta) } e_theta$ on $Gamma_i, ; i=1,2,$ where $varphi_i (theta),psi_i
(theta) $ are $2pi$-periodic smooth function of $theta$, under some
additional condition.
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Mathmatical Subject Classification 35Q30, 76D05