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
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。
Abstract: 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.
文章引用：华嘉乐, 杨凯迪. 最大密度限制下的欧拉方程解的非唯一性[J]. 应用数学进展, 2021, 10(6): 1956-1972. https://doi.org/10.12677/AAM.2021.106206

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