论文标题
不连续应力张量的非牛顿液
Non-Newtonian fluids with discontinuous-in-time stress tensor
论文作者
论文摘要
我们考虑了描述有限域中不可压缩流体流动的方程系统。在考虑的设置中，考奇（Cauchy）应力张量是单调映射，并且具有渐近的$（s-1）$ - 与参数$ s $的增长，具体取决于空间和时间变量。对于时间变量，我们不假定$ s $的任何平滑度，并且假设对空间变量的Log-Hölder连续性。如果材料特性是瞬时的，例如，例如，这种设置是一种自然的选择，例如通过开关电场。我们建立了长时间的弱解决方案的大数据，只要$ s \ ge（3D+2）（d+2）$。
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$ depending on the spatial and time variable. We do not assume any smoothness of $s$ with respect to time variable and assume the log-Hölder continuity with respect to spatial variable. Such a setting is a natural choice if the material properties are instantaneously, e.g. by the switched electric field. We establish the long time and the large data existence of weak solution provided that $s\ge(3d+2)(d+2)$.
