论文标题
稳定stokes问题的最大规律性属性与通过轮廓级联有关
The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade
论文作者
论文摘要
我们处理稳定的Stokes型问题，与牛顿不可压缩的流体通过空间周期性轮廓级联相关。使用的数学模型基于一个空间周期的缩小，由有界的2D域Omega表示。相应的Stokes型问题是通过Stokes方程，连续性方程和三种类型的边界条件来提出的：曲线gamma0和Gamma1上的周期性条件，Dirichlet边界条件伽玛IN和Gamma-in和Gamma-in和人工“无需做任何gampe”的条件。 （见图1.）我们在弱解的水平上解释了最后一个条件满足的意义。我们表明，尽管Omega的域不是平滑的，并且在Omega角的不同类型的边界条件相遇，但所考虑的问题具有强大的解决方案，其所谓最大规则性属性。
We deal with a steady Stokes-type problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade. The used mathematical model is based on the reduction to one spatial period, represented by a bounded 2D domain Omega. The corresponding Stokes-type problem is formulated by means of the Stokes equation, equation of continuity and three types of boundary conditions: the conditions of periodicity on the curves Gamma0 and Gamma1, the Dirichlet boundary conditions Gamma-in and Gamma-p and an artificial "do nothing"-type boundary condition on Gamma-out. (See Fig. 1.) We explain on the level of weak solutions the sense in which the last condition is satisfied. We show that, although domain Omega is not smooth and different types of boundary conditions meet in the corners of Omega, the considered problem has a strong solution with the so called maximum regularity property.
