Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas

Zhiqiang Shao; Huahui Li

doi:10.3934/cpaa.2016041

Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2016041 ◽

2016 ◽

Vol 15 (6) ◽

pp. 2373-2400 ◽

Cited By ~ 8

Author(s):

Zhiqiang Shao ◽

Huahui Li

Keyword(s):

Euler Equations ◽

Chaplygin Gas ◽

Relativistic Euler Equations ◽

Generalized Chaplygin Gas ◽

Vacuum States ◽

Delta Shocks

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Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for polytropic gases

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2009.01.075 ◽

2009 ◽

Vol 355 (2) ◽

pp. 594-605 ◽

Cited By ~ 41

Author(s):

Gan Yin ◽

Wancheng Sheng

Keyword(s):

Euler Equations ◽

Relativistic Euler Equations ◽

Vacuum States ◽

Delta Shocks

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Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-008-0009-x ◽

2008 ◽

Vol 29 (6) ◽

pp. 611-622 ◽

Cited By ~ 12

Author(s):

Gan Yin ◽

Wancheng Sheng

Keyword(s):

Euler Equations ◽

Relativistic Euler Equations ◽

Vacuum States ◽

Delta Shocks

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Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2013.12.025 ◽

2014 ◽

Vol 413 (2) ◽

pp. 800-820 ◽

Cited By ~ 34

Author(s):

Hanchun Yang ◽

Jinhuan Wang

Keyword(s):

Euler Equations ◽

Chaplygin Gas ◽

Modified Chaplygin Gas ◽

Pressure Limit ◽

Isentropic Euler Equations ◽

Vacuum States ◽

Delta Shocks

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Delta-shocks and vacuums in the relativistic Euler equations for isothermal fluids with the flux approximation

Journal of Mathematical Physics ◽

10.1063/1.5001107 ◽

2019 ◽

Vol 60 (1) ◽

pp. 011508 ◽

Cited By ~ 5

Author(s):

Yu Zhang ◽

Yanyan Zhang

Keyword(s):

Euler Equations ◽

Relativistic Euler Equations ◽

Flux Approximation ◽

Delta Shocks

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Limits of Solutions to the Relativistic Euler Equations for Modified Chaplygin Gas by Flux Approximation

Acta Applicandae Mathematicae ◽

10.1007/s10440-019-00286-w ◽

2019 ◽

Vol 169 (1) ◽

pp. 1-32 ◽

Cited By ~ 1

Author(s):

Yu Zhang ◽

Hanchun Yang

Keyword(s):

Euler Equations ◽

Chaplygin Gas ◽

Modified Chaplygin Gas ◽

Relativistic Euler Equations ◽

Flux Approximation

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The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2014.13.2733 ◽

2014 ◽

Vol 13 (6) ◽

pp. 2733-2748 ◽

Cited By ~ 1

Author(s):

Ju Ge ◽

Wancheng Sheng

Keyword(s):

Euler Equations ◽

Chaplygin Gas ◽

Two Dimensional ◽

Generalized Chaplygin Gas ◽

Gas Expansion

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Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6819 ◽

2020 ◽

Vol 44 (2) ◽

pp. 1176-1184

Author(s):

Ka Luen Cheung

Keyword(s):

Global Existence ◽

Euler Equations ◽

Three Dimensional ◽

Chaplygin Gas ◽

Compressible Euler Equations ◽

Generalized Chaplygin Gas ◽

Compressible Euler

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One dimensional piston problem for compressible Euler equations of generalized Chaplygin gas

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106744 ◽

2021 ◽

Vol 112 ◽

pp. 106744

Author(s):

Yongqiang Fan ◽

Lihui Guo ◽

Xingya Fan ◽

Shouke You

Keyword(s):

Euler Equations ◽

Chaplygin Gas ◽

Compressible Euler Equations ◽

Piston Problem ◽

Generalized Chaplygin Gas ◽

One Dimensional ◽

Compressible Euler

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GLOBAL STABILITY OF SOLUTIONS WITH DISCONTINUOUS INITIAL DATA CONTAINING VACUUM STATES FOR THE RELATIVISTIC EULER EQUATIONS

Chinese Annals of Mathematics Series B ◽

10.1142/s0252959905000397 ◽

2005 ◽

Vol 26 (04) ◽

pp. 491-510 ◽

Cited By ~ 2

Author(s):

YACHUN LI ◽

LIBO WANG

Keyword(s):

Initial Data ◽

Global Stability ◽

Euler Equations ◽

Stability Of Solutions ◽

Relativistic Euler Equations ◽

Discontinuous Initial Data ◽

Vacuum States

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Finite-time singularity formation for the original multidimensional compressible Euler equations for generalized Chaplygin gas

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-020-1287-8 ◽

2020 ◽

Vol 71 (2) ◽

Author(s):

Ka Luen Cheung ◽

Sen Wong

Keyword(s):

Euler Equations ◽

Finite Time ◽

Chaplygin Gas ◽

Compressible Euler Equations ◽

Singularity Formation ◽

Time Singularity ◽

Generalized Chaplygin Gas ◽

Compressible Euler ◽

Finite Time Singularity

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