The riemann problem with delta initial data for the one-dimensional chaplygin gas equations

Wang, Zhen; Zhang, Qingling

doi:10.1016/s0252-9602(12)60064-2

Cited by 27 publications

(2 citation statements)

References 15 publications

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“…As for delta shock waves, we refer readers to [19,20,21,30,32], and the references cited therein for more details. We can also see such as [6,17,33] for the related results about the system (1)-(2) with β = 0. In this paper, we are concerned with Chaplygin gas equations with a source term (β = 0) such as damping, friction and relaxation effect.…”

Section: Lihui Guo Tong LI and Gan Yinmentioning

confidence: 78%

The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term

Guo¹,

Li²,

Yin³

2017

Communications on Pure &Amp; Applied Analysis

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We study the vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. The phenomena of concentration and cavitation to Chaplygin gas equations with a friction term are identified and analyzed as the pressure vanishes. Due to the influence of source term, the Riemann solutions are no longer self-similar. When the pressure vanishes, the Riemann solutions to the inhomogeneous Chaplygin gas equations converge to the Riemann solutions to the pressureless gas dynamics model with a friction term.

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Section: Lihui Guo Tong LI and Gan Yinmentioning

confidence: 78%

The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term

Guo¹,

Li²,

Yin³

2017

Communications on Pure &Amp; Applied Analysis

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“…The main difficulty of studying limiting hypersonic flows is a proper definition of Radon measure solutions of initial-boundary value problems of compressible Euler equations. We note that there are many works on the Cauchy problems of unsteady Euler equations of pressureless flow or Chaplygin gas, and other singular hyperbolic conservation laws for initial value problems, mainly motivated by mathematical curiosity (see, for example, [11,12,23,22,28] and references therein). These works present different definitions of measure solutions of hyperbolic conservation laws.…”

Section: Hypersonic-limit Euler Flows Passing Cones 2667mentioning

confidence: 99%

Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies

Jin¹,

Qu²,

Yuan³

2021

CPAA

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<p style="text-indent:20px;">We study steady uniform hypersonic-limit Euler flows passing a finite cylindrically symmetric conical body in the Euclidean space <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^3 $\end{document}</tex-math></inline-formula>, and its interaction with downstream static gas lying behind the tail of the body. Motivated by Newton's theory of infinite-thin shock layers, we propose and construct Radon measure solutions with density containing Dirac measures supported on surfaces and prove the Newton-Busemann pressure law of hypersonic aerodynamics. It happens that if the pressure of the downstream static gas is quite large, the Radon measure solution terminates at a finite distance from the tail of the body. The main difficulty of the analysis is a correct definition of Radon measure solutions. The results are helpful to understand mathematically some physical phenomena and formulas about hypersonic inviscid flows.</p>

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The Riemann problem for the Chaplygin gas equations with a source term

Shen

2015

Z Angew Math Mech

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Key words Chaplygin gas equations, Riemann problem, delta shock wave, Coulomb-like friction term. MSC (2010) 35L65, 35L67, 35B30, 76N10The Riemann solutions for the one-dimensional Chaplygin gas equations with a Coulomb-like friction term are constructed explicitly. It is shown that the delta shock wave appears in the Riemann solutions in some certain situations. The generalized Rankine-Hugoniot conditions of delta shock wave are established and the position, propagation speed and strength of delta shock wave are given, which enables us to see the influence of Coulomb-like friction term on the Riemann solutions for the Chaplygin gas equations clearly. In addition, the relations connected with the area transportation are derived which include mass and momentum transportation.

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The riemann problem with delta initial data for the one-dimensional chaplygin gas equations

Cited by 27 publications

References 15 publications

The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term

The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term

Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies

The Riemann problem for the Chaplygin gas equations with a source term

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