具有最大密度约束的可压缩等熵欧拉系统二维Riemann问题可容许解的非唯一性

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2023-03-01 DOI:10.1142/s0219891623500017

J. Hua, Lirong Xia

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引用次数: 0

摘要

研究了具有最大密度约束的可压缩等熵Euler系统的二维Riemann问题的熵解的唯一性。约束是用一个奇异的压力施加的。给定标准自相似解由一个激波或一个激波和一个稀疏波组成的初始数据，证明存在无限多个可容许的弱解。这将Markfelder和Klingenberg在[S.Markfelder和C.Klingenberg.气体动力学多维等熵系统的Riemann问题，如果它包含冲击，则是不适定的，经典Euler系统的Arch.Ration.Mech.Anal.227（3）（2018）967–994]中的结果扩展到具有最大密度约束的情况。此外，还对这些解的密度进行了一些估计，以描述解在拥塞附近的行为。

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The non-uniqueness of admissible solutions to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint

We investigate the uniqueness of entropy solution to 2D Riemann problem of compressible isentropic Euler system with maximum density constraint. The constraint is imposed with a singular pressure. Given initial data for which the standard self-similar solution consists of one shock or one shock and one rarefaction wave, it turns out that there exist infinitely many admissible weak solutions. This extends the result of Markfelder and Klingenberg in [S. Markfelder and C. Klingenberg, The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock, Arch. Ration. Mech. Anal. 227(3) (2018) 967–994] for classical Euler system to the case with maximum density constraint. Also some estimates on the density of these solutions are given to describe the behavior of solutions near congestion.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.