数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (4): 855-875.doi: 10.1016/S0252-9602(15)30025-4

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SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS

陈宇, 周忆   

  • 收稿日期:2015-02-04 出版日期:2015-07-01 发布日期:2015-07-01

SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS

Yu CHEN, Yi ZHOU   

  1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • Received:2015-02-04 Online:2015-07-01 Published:2015-07-01

摘要:

In this paper, we establish the existence of four families of simple wave solution for two dimensional compressible full Euler system in the self-similar plane. For the 2×2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4×4 non-reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0123 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.

关键词: simple waves, Euler equations, characteristic decomposition

Abstract:

In this paper, we establish the existence of four families of simple wave solution for two dimensional compressible full Euler system in the self-similar plane. For the 2×2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4×4 non-reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0123 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane.

Key words: simple waves, Euler equations, characteristic decomposition

中图分类号: 

  • 35C06