论文标题
稳定stokes问题的最大规律性属性与通过$ l^r $ framework流过的cascade相关
The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in $L^r$-framework
论文作者
论文摘要
该论文处理了Stokes问题，与通过空间周期性轮廓级联流动的流动流动有关。我们使用[32]（$ l^2 $ -framework中的最大规则属性）和[33]（$ W^{1，r} $中的弱溶解度），并将最大规律性属性上的发现扩展到一般$ l^r $ -framework（以$ 1 <r <r <\ f infty $）。利用将一个空间周期$ω$减少到一个空间周期，通过三种类型的边界条件来提出问题：曲线周期性的条件$γ_0$和$γ_1$，$γ_{\ rm in} $ in} $和$γ_p$和$γ_p$的dirichlet边界条件和“ do do do do do do note” $ type of of $ quard of。我们表明，尽管域$ω$不是平滑的，并且在$ \partialΩ$的顶点中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，具有“平滑”数据的最大规则性属性。我们解释了“无所事事”边界条件在弱和强大解决方案中都满足的意义。
The paper deals with the Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. We use results from [32] (the maximum regularity property in the $L^2$-framework) and [33] (the weak solvability in $W^{1,r}$), and extend the findings on the maximum regularity property to the general $L^r$-framework (for $1<r<\infty$). Using the reduction to one spatial period $Ω$, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves $Γ_0$ and $Γ_1$, the Dirichlet boundary conditions on $Γ_{\rm in}$ and $Γ_P$ and an artificial "do nothing"-type boundary condition on $Γ_{\rm out}$ (see Fig. 1). We show that, although domain $Ω$ is not smooth and different types of boundary conditions "meet" in the vertices of $\partialΩ$, the considered problem has a strong solution with the maximum regularity property for "smooth" data. We explain the sense in which the "do nothing" boundary condition is satisfied for both weak and strong solutions.
