论文标题
Stokes System的弱解决方案，用于可压缩的非牛顿流体，无界差异
Weak solutions for the Stokes system for compressible non-Newtonian fluids with unbounded divergence
论文作者
论文摘要
我们研究了某个部分微分方程系统的弱解的存在，对小雷诺数的可压缩非牛顿液的行为进行了建模。我们构建了薄弱的解决方案，尽管缺乏$ l^\ infty $估计在速度场的分歧上。结果是通过将奇异算子的规则性理论与$ bmo $函数的一定对数积分不平等相结合，这使我们能够调整（Feireisl等，2015）的方法，以使速度更加轻松。
We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack of the $L^\infty$ estimate on the divergence of the velocity field. The result was obtained by combining the regularity theory for singular operators with a certain logarithmic integral inequality for $BMO$ functions, which allowed us to adjust the method from (Feireisl et al., 2015) to more relaxed conditions on the velocity.
