标题： 不可压缩Stokes问题带有Tresca摩擦条件的正则化 显示英文标题

标题： A regularization of incompressible Stokes problem with Tresca friction condition

摘要： 在本文中，我们引入并研究了一种处理具有Tresca型非线性边界条件的Stokes问题的模型。 我们提出了一种新的不可压缩流体正则化方法，即假设散度为$\nabla \cdot {\bf u}\in [-\epsilon,\,\epsilon]$，这导致一类约束椭圆变分不等式。 我们利用不动点策略证明了解的存在性和唯一性，并将问题重新表述为一个等价的约束最小化问题。 我们将ADMM应用于最小化问题，并提供了一些算法。 显示英文摘要

摘要： In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the divergence $\nabla \cdot {\bf u}\in [-\epsilon,\,\epsilon]$ which leads to class of constrained elliptic variational inequalities. We use a fixed point strategy to show the existence and uniqueness of a solution and we reformulate the problem as an equivalent constrained minimization problem. An ADMM is applied to the minimization problem and some algorithm are provided.