论文标题
LR-Framework中通过配置文件级联的流量相关的弱stokes问题
The weak Stokes problem associated with a flow through a profile cascade in Lr-framework
论文作者
论文摘要
我们研究了LR-Framework中通过空间周期性的级联级联反应，与牛顿不可压缩的流体流动有关的弱稳态问题。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问题是通过三种类型的边界条件来提出的：边界的“下部”和“上部”部分的周期性条件，“流入”和“流入”的Dirichlet边界条件以及轮廓上的Dirichlet边界条件以及人为的“无所作为” - 类型在“流出”上的边界条件。在给定数据的适当假设下，我们证明了w^{1，r}（Omega）中弱解决方案的存在和唯一性及其对数据的持续依赖性。我们解释了“流出”上满足“流出”边界条件的意义。
We study the weak steady Stokes problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade, in the Lr-framework. The used mathematical model is based on the reduction to one spatial period, represented by a bounded 2D domain Omega. The corresponding Stokes problem is formulated by means of three types of boundary conditions: the conditions of periodicity on the "lower" and "upper" parts of the boundary, the Dirichlet boundary conditions on the "inflow" and on the profile and an artificial "do nothing"--type boundary condition on the "outflow". Under appropriate assumptions on the given data, we prove the existence and uniqueness of a weak solution in W^{1,r}(Omega) and its continuous dependence on the data. We explain the sense in which the "do nothing" boundary condition on the "outflow" is satisfied.
