In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

中文翻译：

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具有Tresca边界条件的自由边界问题解的渐近行为

在本文中，我们研究了具有Tresca边界条件的薄域中不可压缩的Herschel-Bulkley流体的渐近行为。我们研究了趋于零时的极限，证明了流体速度和压力等未知数的收敛性，并得到了极限问题和特定的雷诺方程。