带有Power-Law型粘性项的可压缩非牛顿流的光滑解

Classical Solutions to the Compressible Non-Newtonian Fluids with Power-Law Viscous

本文研究一维有界区间上的可压非牛顿流体模型。在初始密度有正下界的情况下,通过构造逼近解,应用能量估计,得到了带有Power-Law结构粘性项的非牛顿流模型初边值问题光滑解的局部存在性。

In this paper,a one-dimensional compressible non-Newtonian fluid model on a bounded interval is studied.If the initial density has a positive lower bound,the local existence of the classical solutions for the initial boundary value problem of a non-Newtonian fluid model with Power-Law viscous is proved by constructing approximate solutions and applying energy estimation.