We study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady Oseen model for a generalized Newtonian incompressible fluid. A variational‐hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier‐Fujita slip condition, and the threshold slip and leak condition of frictional type.

中文翻译：

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具有单边和摩擦类型边界条件的稳定Oseen流的一类新的变分-半变分不等式

我们研究了自反Banach空间中的一类新的椭圆变分半偏不等式。基于一个包含Clarke的亚微分类型的算子的相斥性结果，我们证明了解的存在。然后，我们将此结果应用于广义牛顿不可压缩流体的稳定Oseen模型的数学分析。推导了流动问题的变分半变分不等式，并获得了存在弱解的充分条件。混合边界条件包括单边边界条件，Navier滑动条件，非线性Navier-Fujita滑动条件的非单调版本以及阈值滑动和摩擦类型的泄漏条件。