论文标题
一类可压缩的非牛顿流体方程的适应性
Well-posedness for a class of compressible non-Newtonian fluids equations
论文作者
论文摘要
本文的目的是处理一类非牛顿流体动力学方程式的适应性问题。这些方程组通常用于描述出现在自然，工业和生物学中的各种复杂模型。描述此类流体运动的方程式的特征是将应力状态与变形率有关的非线性本构定律。我们向两个重要模型的强大解决方案展示了当地的存在和独特性：Power Law Model和Bingham模型。虽然我们的第一个模型的结果在周期性域$ω= \ mathbb {r}^3中保存，但在第二个模型上获得的结果仅限于一维情况。这是因为宾厄姆的本构定律是由于相变而出现的，这可能是在流动自然变化时出现的，尤其是从液体运动到刚性运动，反之亦然。此属性降低了在更高维空间中向这种系统显示平滑解决方案的概率。
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and biology. The equations describing the motion of such fluids are characterized by a non-linear constitutive law relating the state of stress to the rate of deformation. We show the local-in-time existence and uniqueness of strong solutions to two important models: the Power Law model and the Bingham model. While our result for the first model holds over a periodic domain $Ω=\mathbb{R}^3,$ the result obtained on the second model is limited to the one-dimensional case. This is because Bingham's constitutive law is discontinuous due to phase transition that may appear during the time when flows change nature, particularly from liquid motion to rigid motion and vice-versa. This property reduces the probability of showing smooth solutions to such a system in higher dimension space.
