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Global existence for a one-dimensional non-relativistic Euler model with relaxation
Portugaliae Mathematica ( IF 0.8 ) Pub Date : 2020-09-09 , DOI: 10.4171/pm/2044
Shuyang Xiang 1 , Yangyang Cao 2
Affiliation  

We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced random choice method called Glimm method which preserves the fluid equilibria and we construct a sequence of approximate weak solutions which converges to the exact weak solution of the initial value problem, based on the construction of exact solutions of the generalized Riemann problem associated with initially piecewise steady state solutions.

中文翻译:

具有松弛的一维非相对论欧拉模型的整体存在

我们研究一类带有源项的欧拉方程的初值问题。我们的主要结果是存在一个全局及时的弱解,其总变化以定义域为界,从而允许存在冲击波。我们的证明依赖于一种称为Glimm方法的平衡良好的随机选择方法,该方法保留了流体平衡,并在构造方程组的精确解的基础上构造了一系列近似的弱解,这些解收敛到初始值问题的精确弱解。与最初的分段稳态解相关的广义Riemann问题。
更新日期:2020-09-10
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