最大密度限制下的欧拉方程解的非唯一性  

Nonuniqueness of Solutions of Euler Equation with Maximum Density Restraint

作　　者：华嘉乐 杨凯迪 

机构地区：[1]东华大学理学院,上海

出　　处：《应用数学进展》2021年第6期1956-1972,共17页Advances in Applied Mathematics

摘　　要：在本文中,我们考虑了带有最大密度限制的等熵可压欧拉方程的二维黎曼问题,这一最大密度限制通过带有奇性的压强项实现。对适当构造的黎曼问题初值,证明了系统存在无穷多个满足经典熵条件的可容许弱解,这推广了Elisabetta Chiodaroli和OndřejKreml对等熵可压欧拉方程的结果。In this paper we consider the 2D Riemann problem of isentropic compressible Euler equations with a singular pressure law , which imposes a stiff constraint on the maximum density. With a suitably constructed Riemann data, we prove that there exist infinitely many admissible weak solutions to the system satisfying the classical entropy condition. This is a generalization of Elisabetta Chiodaroli and OndřejKreml’s results on isentropic compressible Euler equations.

关 键 词：等熵可压欧拉方程 非唯一性 黎曼问题 可容许弱解 熵条件 

分 类 号：O17[理学—数学]