一维空间中可压缩变指数增长非牛顿流体模型的强解

The Strong Solutions to the Compressible Non-Newtonian Fluids with Variable Exponential Growth in One Dimension

摘要: 本文在一维有界区间上研究了一类可压缩变指数增长的流体模型。此类模型是带有p(x)-Lapalace粘性项的可压缩非牛顿流体模型。我们通过构造逼近解，应用能量估计，克服变指数带来的强非线性性质，得到了非牛顿粘性参数1 < p(x) < 2，且初始密度存在真空的情况下，此类可压缩非牛顿流体模型初边值问题强解的存在唯一性。

Abstract: In this paper, a class of compressible non-Newtonian fluid with variable exponential is studied on one-dimensional bounded interval. This model is a compressible non-Newtonian fluid model with a p(x)-Laplace viscosity term. By constructing an approximate solution and applying energy estimation to overcome the nonlinear property of strong viscous term, we obtain the existence and uniqueness of the strong solution to electroviscous fluid under the condition of the non-Newtonian viscous parameter 1 < p(x) < 2 and vacuum at the initial density.

文章引用：苏敏, 佟丽宁. 一维空间中可压缩变指数增长非牛顿流体模型的强解[J]. 理论数学, 2020, 10(4): 362-373. https://doi.org/10.12677/PM.2020.104046

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