We study the generalized stationary Stokes system in a bounded domain in the plane equipped with perfect slip boundary conditions. We show natural stability results in oscillatory spaces, i.e., Hölder spaces and Campanato spaces, including the border-line spaces of bounded mean oscillations (BMO) and vanishing mean oscillations (VMO). In particular, we show that, under appropriate assumptions, gradients of solutions are globally continuous. Since the stress tensor is assumed to be governed by a general Orlicz function, our theory includes various cases of (possibly degenerate) shear thickening and shear thinning fluids; including the model case of power law fluids. The global estimates seem to be new even in the case of the linear Stokes system. We include counterexamples that demonstrate that our assumptions on the right-hand side and on the boundary regularity are optimal.

中文翻译：

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具有完美滑移边界条件的非牛顿流体的整体连续性和BMO估计

我们在配备完善滑移边界条件的平面上的有界域中研究广义平稳Stokes系统。我们显示了振荡空间（即Hölder空间和Campanato空间）的自然稳定性结果，包括有界平均振荡（BMO）和消失平均振荡（VMO）的边界线空间。特别是，我们表明，在适当的假设下，解决方案的梯度是全局连续的。由于假定应力张量受一般的Orlicz函数控制，因此我们的理论包括剪切增稠和剪切稀化流体的各种情况（可能是简并的）。包括幂律流体的模型案例。即使在线性斯托克斯系统的情况下，全局估计似乎也是新的。