期刊
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
卷 44, 期 12, 页码 9876-9898出版社
WILEY
DOI: 10.1002/mma.6476
关键词
boundary-domain integral equations; equivalence; invertibility; parametrix; Stokes equations
资金
- Alexander von Humboldt Foundation [3.4-ETH/1144171]
This paper considers the Dirichlet and Neumann boundary value problems for the steady-state Stokes system of partial differential equations for a compressible viscous fluid with variable viscosity coefficient in a two-dimensional bounded domain. It shows the equivalence of the BDIE systems to the Dirichlet and Neumann BVPs and the invertibility of the corresponding boundary-domain integral operators in appropriate Sobolev spaces. The special properties of BDIEs in the two-dimensional case, compared to the three dimension, are due to the logarithmic term in the parametrix for the associated partial differential equations.
In this paper, the Dirichlet and Neumann boundary value problems for the steady-state Stokes system of partial differential equations for a compressible viscous fluid with variable viscosity coefficient is considered in two-dimensional bounded domain. Using an appropriate parametrix, this problem is reduced to a system of direct segregated boundary-domain integral equations (BDIEs). The BDIEs in the two-dimensional case have special properties in comparison with the three dimension because of the logarithmic term in the parametrix for the associated partial differential equations. Consequently, we need to set conditions on the function spaces or on the domain to ensure the invertibility of corresponding parametrix-based hydrodynamic single layer and hypersingular potentials and hence the unique solvability of BDIEs. Equivalence of the BDIE systems to the Dirichlet and Neumann BVPs and the invertibility of the corresponding boundary-domain integral operators in appropriate Sobolev spaces are shown.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据