三维有界区域中非牛顿可压缩流体的广义解

考虑流体的偏应力张量分量与速度梯度为非线性关系的情况，本构方程仅依赖于速度梯度的一阶导数。对满足强制性条件，以及增长性条件 的非牛顿粘性可压缩流体在三维有界区域中的流动进行了研究，其中和为正常数，为速度梯度张量, 是偏应力张量，为的分量，它依赖于速度梯度张量。文章利用构造近似解和极限的过程证明了三维有界区域中非牛顿可压缩流体广义解的存在性，所用的证明方法为能量方法。

Generalized solution for a non-Newtonian viscous compressible fluid in 3D-bounded domains

In view of the non-linear relation between the hefts of the partial stress tensor and the velocity gradient of the fluid, the intrinsic equation only depends on the first order differential coefficient of the velocity gradient. We have studied a model of a non-Newtonian viscous compressible fluid in 3D bounded domains, in which the viscous part of the stress tensor satisfies the coerciveness condition and the values of the growth condition . , are positive constants. Here is the tensor of the velocity gradient, is the strain tensor and ,which depends on the tensor of the velocity gradient, is the hefts of .By means of deriving the approximate solution and a process of approaching iteration, we have shown that a general solution exists for a non-Newtonian compressible fluid in 3D bounded domains. The proof is based on an elementary energy method.