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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >On the dual-mixed formulation for an exterior stokes problem
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On the dual-mixed formulation for an exterior stokes problem

机译：关于外部斯托克斯问题的双重混合配方

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This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & Nédélec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the well-known Babu?ka-Brezzi theory: in particular, the well-posedness of the formulation will be established. This paper is concerned with a dual-mixed formulation for a three dimensional exterior Stokes problem via boundary integral equation methods. Here velocity, pressure and stress are the main unknowns. Following a similar analysis given recently for the Laplacian, we are able to extend the classical Johnson & Nédélec procedure to the present case, without assuming any restrictive smoothness requirement on the coupling boundary, but only Lipschitz-continuity. More precisely, after using the incompressibility condition to eliminate the pressure, we consider the resulting velocity-stress approach with a Neumann boundary condition on an annular bounded domain, and couple the underlying equations with only one boundary integral equation arising from the application of the normal trace to the Green representation formula in the exterior unbounded region. As a result, we obtain a saddle point operator equation, which is then analyzed by the wellknown Babu?ka-Brezzi theory: in particular, the well-posedness of the formulation will be established.
机译：本文涉及通过边界积分方程方法的三维外部斯托克斯问题的双重混合公式。在这里，速度，压力和应力是主要未知数。根据最近对拉普拉斯算子进行的类似分析，我们能够将经典的Johnson＆Nédélec程序扩展到当前情况，而无需假设对耦合边界的任何限制平滑度，而仅假设Lipschitz连续性。更精确地讲，在使用不可压缩条件消除压力之后，我们考虑在环形有界域上使用带有Neumann边界条件的结果速度应力方法，并将基础方程与仅由法线应用引起的边界积分方程耦合跟踪到外部无界区域中的Green表示公式。结果，我们获得了一个鞍点算子方程，然后用众所周知的Babu？ka-Brezzi理论对其进行分析：特别是，将确定该公式的适定性。本文涉及通过边界积分方程法的三维外部斯托克斯问题的双重混合公式。在这里，速度，压力和应力是主要未知数。根据最近对拉普拉斯算子进行的类似分析，我们能够将经典的Johnson＆Nédélec程序扩展到当前情况，而无需假设对耦合边界的任何限制平滑度，而仅假设Lipschitz连续性。更精确地讲，在使用不可压缩条件消除压力之后，我们考虑在环形有界域上使用带有Neumann边界条件的结果速度应力方法，并将基础方程与仅由法线应用引起的边界积分方程耦合跟踪到外部无界区域中的Green表示公式。结果，我们获得了一个鞍点算子方程，然后用著名的Babu？ka-Brezzi理论对其进行分析：特别是，将建立该公式的适定性。

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