Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow condition

スポンサーリンク

概要

• 論文の詳細を見る

• 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.

• 東京大学の論文

著者

• Ukai Seiji

  Department Of Mathematical And Computing Sciences Tokyo Institute Of Technology

• Ukai Seiji

  Department Of Applied Mathematics Yokohama National University

• Morimoto Hiroko

  Department Of Mathematics School Of Science And Technology Meiji University

関連論文

• Genetic Influences in Mouse Spermatogonial Stem Cell Self-Renewal
• On the Cauchy problem of the Boltzmann Equation with a Soft Potential
• The Boltzmann-Grad Limit and Cauchy-Kovalevskaya Theorem
• Perturbation of the Navier-Stokes flow in an annular domain with the non-vanishing outflow condition
• Steady Solutions of the Boltzmann Equation for a Gas Flow past an Obstacle, II. Stability : Dedicated to Professor Mizohata on his 60th anniversary
• Convex entropy function and symmetrization of the relativistic Euler equation(Mathematical Analysis of Phenomena in fluid and Plasma Dynamics)
• Recent topics on the compressible Euler equation(Mathematical Fluid Mechanics and Modeling)
• Global weak solutions of the compressible Euler equation with spherical symmetry (II)
• The Global Weak Solutions of the Compressible Euler Equation with Spherical Symmetry(Evolution Equations and Nonlinear Problems)
• On the Singular Limits of the Boltzmann Equation(Mathematical Fluid Mechanics and Modeling)
• A Generalized Analysis of Rossi-α Experiment

もっと見る 閉じる

スポンサーリンク