SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS

doi:10.1016/S0252-9602(15)30025-4

Abstract

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 λ₀=λ₁,λ₂,λ₃ 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

CLC Number:

35C06

Yu CHEN, Yi ZHOU. SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS[J].Acta mathematica scientia,Series B, 2015, 35(4): 855-875.

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