We consider steady flows of shear thinning fluids in bounded domains under the action of external forces and Dirichlet boundary conditions. For a power-law index $q\in (2d∕(d+2),3d∕(d+2)]$, we construct weak solutions to the nonhomogeneous boundary value problem assuming that the boundary data is small enough. Moreover, under the restriction $q\in ((2d-1)∕d,2)$, $d=2,3$, and extra regularity for the boundary data, we construct weak solutions by extending the tangential part of the velocity at the boundary in such a way that it is possible to partially control the inertial term. This imposes restrictions only on the size of the normal component of the boundary data.

我们考虑在外力和Dirichlet边界条件的作用下，有限域内的剪切稀化流体的稳定流动。对于幂律索引$q\in （\mathrm{2个}d∕（d+\mathrm{2个}），3d∕（d+\mathrm{2个}）]$，假设边界数据足够小，我们为非齐次边值问题构造了弱解。而且，在限制下$q\in （（\mathrm{2个}d-\mathrm{1个}）∕d，\mathrm{2个}）$， $d=\mathrm{2个}，3$，以及边界数据的额外规则性，我们通过扩展边界处速度的切向部分来构造弱解，从而可以部分控制惯性项。这仅对边界数据的法线分量的大小施加了限制。