A coherent analysis of Stokes flows under boundary conditions of friction type
A coherent analysis of Stokes flows under boundary conditions of friction type
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DOI：
10.1016/s0377-0427(02)00520-4
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发表时间：
2002-12
影响因子：
2.4
通讯作者：
H. Fujita
中科院分区：
文献类型：
--
作者：
H. Fujita
本文讨论了粘性不可压缩流体在摩擦型边界条件下的定常流动和非定常流动，这些边界条件是类似于弹性力学中所谓的西诺里尼边界条件的某些非线性边界条件。我们假设流动由线性Stokes方程控制，而边界条件是非线性的。从方法论的角度出发，用变分不等式理论研究定常流动的相关边值问题，用非线性半群理论证明非定常流动初边值问题的适定性。从应用的角度，我们提到了最初的动机，并包括了一些新的推广，如各向异性摩擦和非齐次边值的情况。
This paper is concerned with the stationary and nonstationary flow of viscous incompressible fluid under boundary conditions of friction type, which are certain nonlinear boundary conditions similar to the so-called Signorini boundary condition in elasticity. We assume that the flow is governed by the linear Stokes equation, while the boundary condition is nonlinear. From the methodological viewpoint, the analysis is carried out in a coherent way, starting from study of the related boundary value problems for the stationary flow by means of the theory of variational inequalities, and getting to wellposedness of the initial boundary value problems for the nonstationary flow by means of the nonlinear semigroup theory. From the viewpoint of applications, we mention original motivations and include some new generalizations like the cases of anisotropic friction and inhomogeneous boundary value.