论文标题
非等温非牛顿液：固定案例
Non-isothermal non-Newtonian fluids: the stationary case
论文作者
论文摘要
非牛顿不可压缩流体的固定navier-stokes方程与固定热方程式结合，并受到Dirichlet类型边界条件的约束。粘度应该取决于温度，压力取决于适合的功率定律，具体取决于$ p \ in（1,2）$（剪切稀薄的情况）。对于这个问题，我们确定了弱解决方案的存在，并证明了Navier-Stokes和Stokes案例的一些规律性结果。然后，通过FEM方案近似Carreau Power Law的后一种情况，并获得了一些错误估计。然后，通过一些二维数值实验来验证此类估计。
The stationary Navier-Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet type boundary conditions. The viscosity is supposed to depend on the temperature and the stress depends on the strain through a suit-able power law depending on $p \in (1,2)$ (shear thinning case). For this problem we establish the existence of a weak solution as well as we prove some regularity results both for the Navier-Stokes and the Stokes cases. Then, the latter case with the Carreau power law is approximated through a FEM scheme and some error estimates are obtained. Such estimates are then validated through some two-dimensional numerical experiments.
