We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by the measure-valued solutions for the inviscid (Euler) system. We show the existence as well as the weak–strong uniqueness property in the class of dissipative solutions. Finally, the dissipative solution enjoying certain extra regularity coincides with a strong solution of the same problem.

中文翻译：

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关于描述不可压缩粘性流体的方程的一类广义解

我们考虑一类粘性流体，其粘性应力对对称速度梯度具有一般的单调依赖性。我们将耗散解决方案的概念引入到相关的初始边值问题，该问题由无粘性（Euler）系统的量值解决方案启发而来。我们在耗散解的类别中显示了存在性以及弱强唯一性。最后，具有一定规律性的耗散解与对同一问题的强解相吻合。