We study the stationary flow of an incompressible non-Newtonian fluid of Bingham type, mathematically described by means of a nonlinear boundary value problem governed by PDEs. The variational formulation which we propose is a mixed variational problem with Lagrange multipliers. First, we obtain existence, uniqueness, and stability results into an abstract framework. Then, we discuss the well-posedness of the mechanical model based on the auxiliary abstract results.

中文翻译：

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关于Bingham模型的Lagrange乘子的弱可解性

我们研究了不可压缩的Bingham型非牛顿流体的平稳流动，该流体通过PDE控制的非线性边值问题在数学上进行了描述。我们提出的变分公式是拉格朗日乘数的混合变分问题。首先，我们将存在性，唯一性和稳定性结果放入一个抽象框架中。然后，我们基于辅助抽象结果讨论了力学模型的适定性。