混合气体Euler方程解的整体存在性及大时间行为
The Global Existence and Large Time Behavior of the Solution of Euler Equation of Mixed Gas

作者: 李娌芝 , 官心果 :云南民族大学,数学与计算机科学学院,云南 昆明; 王清涛 :西南林业大学,机械与制造工程学院,云南 昆明;

关键词: Euler方程组Maxwell-Stefan方程整体存在性大时间行为Euler Equations Maxwell-Stefan Equations Global Existence Long Time Behavior

摘要: 该文研究了三种气体Euler方程在小初值的情况下解的整体存在性及大时间行为问题。本文的主要内容是定理1.1的证明。首先给出引理3.1,对于 充分小,利用Hölder不等式,Young不等式等计算方法将未知函数 关于x的导数用 关于时间t的导数进行估计。然后用标准能量估计方法,对浓度通量 估计;最后构造 函数与 等价,证明出 满足一致有界且指数衰减速率,从而得到 也是一致有界且指数衰减速率。

Abstract: In this paper, the global existence and large time behavior problem of three gases of Euler equation in the small initial value are studied. The main content of this chapter is the proof of theorem 1.1. First of all, we first give a lemma 3.1 for a sufficiently small. Using the Hölder inequality, Young inequality and other calculation methods, the derivative of unknown function with respect to x is estimated using the derivative of with respect to time t. Then, standard energy estimation method is used to estimate the concentration of flux . Finally, by constructing the and function equivalent, we prove meets uniformly bounded and exponential decay rate, so as to get is uniformly bounded and exponential decay rate. 

文章引用: 李娌芝 , 王清涛 , 官心果 (2018) 混合气体Euler方程解的整体存在性及大时间行为。 应用数学进展, 7, 1203-1211. doi: 10.12677/AAM.2018.79140

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