The Riemann problem for the two-dimensional zero-pressure Euler equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Pang, Yicheng¹ 

[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China

关键词: Zero-pressure Euler equations;    Riemann problem;    Delta shock wave;    Contact discontinuity;    Vacuum;   

DOI  :  10.1016/j.jmaa.2018.12.046

来源: Elsevier

【 摘 要 】

The Riemann problem for the two-dimensional zero-pressure Euler equations is considered. The initial data are constant values in each quadrant, which satisfy an assumption that each initial discontinuity projects only one two-dimensional wave. The phenomenon of two-dimensional delta shock wave with a Dirac delta function in both density and internal energy is identified. Both generalized Rankine-Hugoniot relation and entropy condition for this type of two-dimensional delta shock wave are proposed. The qualitative behavior of entropy solutions to this relation with certain special initial data is established. Based on these preparations, we obtain twenty-three explicit solutions and their corresponding criteria. In particular, the Mach-reflection-like patterns arise in the exact solutions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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