Stability of the Isentropic Riemann Solutions of the Full Multidimensional Euler System
Stability of the Isentropic Riemann Solutions of the Full Multidimensional Euler System
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DOI：
10.1137/140999827
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
E. Feireisl;Ondřej Kreml;A. Vasseur
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文献类型：
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作者：
E. Feireisl;Ondřej Kreml;A. Vasseur
考虑描述无粘非等温气体时间演化的完整欧拉方程组。我们证明了一维（1-D）Riemann问题的稀疏波解是稳定的，特别是唯一的，在类的所有有界弱解相关联的多维问题。这可以看作是最近构造的凸积分方法的1-D冲击波所产生的物理上允许的解决方案的非唯一性结果的对应。
We consider the complete Euler system describing the time evolution of an inviscid nonisothermal gas. We show that the rarefaction wave solutions of the one-dimensional (1-D) Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multidimensional problem. This may be seen as a counterpart of the nonuniqueness results of physically admissible solutions emanating from 1-D shock waves constructed recently by the method of convex integration.