Riemann problem for the relativistic Chaplygin Euler equations

Cheng, Hongjun; Yang, Hanchun

doi:10.1016/j.jmaa.2011.04.017

Cited by 45 publications

(23 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this section, we briefly review the Riemann solutions of and with initial data

(v (x MathClass-punc, 0) MathClass-punc, ρ (x MathClass-punc, 0)) MathClass-rel= (v_{MathClass-bin\pm} MathClass-punc, ρ_{MathClass-bin\pm}) MathClass-punc, MathClass-bin\pm x MathClass-rel> 0 MathClass-punc,

where ρ ± > 0, the detailed study of which can be found in . For more details about the Riemann problem for hyperbolic conservation laws, please see .…”

Section: Preliminariesmentioning

confidence: 99%

“…For system (1.1) and (1.7), Cheng et al [26] solved the Riemann problem and established the existence and uniqueness of delta shock solutions. In this model, the formation of delta shock exhibits some phenomena during the evolution of the universe, such as the formation and development of the black hole, the boom and inflation of the universe and so on.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

Guo

Zhang

Yin

2014

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large timeasymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter tends to zero.

show abstract

“…In this section, we briefly review the Riemann solutions of and with initial data

(v (x MathClass-punc, 0) MathClass-punc, ρ (x MathClass-punc, 0)) MathClass-rel= (v_{MathClass-bin\pm} MathClass-punc, ρ_{MathClass-bin\pm}) MathClass-punc, MathClass-bin\pm x MathClass-rel> 0 MathClass-punc,

where ρ ± > 0, the detailed study of which can be found in . For more details about the Riemann problem for hyperbolic conservation laws, please see .…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

Guo

Zhang

Yin

2014

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

show abstract

“…The Euler system of conservation laws of energy and momentum for a Chaplygin gas in special relativity reads (cf. ):

({, \begin{matrix} falsenonefalsearray \\ arrayaxis \partial_{t} (MathClass-open(p + ρ c^{2} MathClass-close) \frac{v^{2}}{c^{2} MathClass-open(c^{2} - v^{2} MathClass-close)} + ρ) + \partial_{x} (MathClass-open(p + ρ c^{2} MathClass-close) \frac{v}{c^{2} - v^{2}}) = 0, \\ arrayaxis \partial_{t} (MathClass-open(p + ρ c^{2} MathClass-close) \frac{v}{c^{2} - v^{2}}) + \partial_{x} (MathClass-open(p + ρ c^{2} MathClass-close) \frac{v^{2}}{c^{2} - v^{2}} + p) = 0, \end{matrix})

where ρ , p and v represent the proper energy density, the pressure and the particle speed, respectively. The equations of state is

p (ρ) MathClass-rel= MathClass-bin- \frac{1}{ρ} MathClass-punc, for ρ MathClass-rel> 0 MathClass-punc.

System models the dynamics of plane waves in special relativistic fluids in a two‐dimensional Minkowski time‐space ( x 0 , x 1 ):

div T M...

…”

Section: Applicationsmentioning

confidence: 99%

“…The Euler system of conservation laws of energy and momentum for a Chaplygin gas in special relativity reads (cf. [34][35][36]…”

Section: The Relativistic Euler Equations For Chaplygin Gasesmentioning

confidence: 99%

Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

Shao

2013

Math Methods in App Sciences

View full text Add to dashboard Cite

“…Y. Brenier [1] studied the one dimensional Riemann problems and obtained the solutions with concentration. Cheng and Yang [9] studied the Riemann problem for the relativistic Chaplygin Euler equations. In addition, D. Serre [40] studied the interaction of pressure waves for the 2-D isentropic irrotational Chaplygin gas.…”

Section: Introductionmentioning

confidence: 99%

The Riemann problem for one dimensional generalized Chaplygin gas dynamics

Wang

2013

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

a b s t r a c tThe Riemann problem for one dimensional generalized Chaplygin gas dynamics is considered. Its two characteristic fields are genuinely nonlinear, but the nonclassical solutions appear. The formation of mechanism for δ-shock is analyzed, that is the oneshock curve and the two-shock curve do not intersect each other in the phase plane. The Riemann solutions are constructed, and the generalized Rankine-Hugoniot conditions and the δ-entropy condition are clarified. By the interaction of the delta-shock wave with the elementary waves, the generalized Riemann problem for this system is presented.Furthermore, by studying the limits of the solutions as perturbed parameter ε approaches zero, one can observe that the Riemann solutions are stable for such perturbations of the initial data. Some numerical simulations are given to illustrate our analysis.Crown

show abstract

Riemann problem for the relativistic Chaplygin Euler equations

Cited by 45 publications

References 30 publications

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

The Riemann problem for one dimensional generalized Chaplygin gas dynamics

Contact Info

Product

Resources

About