×

Simple waves of the two dimensional compressible Euler system for a class of pressure laws. (English) Zbl 07453768

Summary: In this paper, we consider a two-dimensional compressible Euler system for a class of pressure laws Chen (Arch Ration Mech Anal 166:81–98, 2003), and use the characteristic decomposition to establish that any wave adjacent to a constant state must be a simple wave. These results are generalization of the well-known theorem on reducible equations in Courant and Friedrichs’s monograph Courant, ansd Friedrichs (Supersonic flow and shock waves, Interscience, New York, 1948).

MSC:

35Q31 Euler equations
35L65 Hyperbolic conservation laws
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] G. Q.Chen, Philippe G. LeFloch, Existence theory for the isentropic Euler equations, Arch. Ration. Mech. Anal., 166 (2003), 81-98. · Zbl 1027.76043
[2] Chen, X.; Zheng, YX, The interaction of rarefaction waves of the two-dimensional Euler equations, Indiana Univ. Math. J., 59, 231-256 (2010) · Zbl 1203.35167
[3] Courant, R.; Friedrichs, KO, Supersonic flow and shock waves (1948), New York: Interscience, New York · Zbl 0041.11302
[4] Dai, ZH; Zhang, T., Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal., 155, 277-298 (2000) · Zbl 1007.76072
[5] Hu, YB; Sheng, WC, Characteristic decomposition of the 2 × 2 quasilinear strictly hyperbolic systems, Appl. Math. Lett., 25, 3, 262-267 (2012) · Zbl 1246.35126
[6] Lax, P., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., 5, 611-613 (1964) · Zbl 0135.15101
[7] Li, MJ; Zheng, YX, Semi-hyperbolic patches of solutions of the two-dimensional Euler equations, Arch. Ration. Mech. Anal., 201, 1069-1096 (2011) · Zbl 1270.76064
[8] Li, JQ; Zheng, YX, Interaction of rarefaction waves of the two-dimensional self-similar Euler equations, Arch. Ration. Mech. Anal., 193, 623-657 (2009) · Zbl 1170.76021
[9] Li, JQ; Zheng, YX, Interaction of four rarefaction waves in the bi-symmetric class of the two-dimensional Euler equations, Comm. Math. Phys., 296, 303-321 (2010) · Zbl 1193.35140
[10] Li, JQ; Zhang, T.; Zheng, YX, Simple waves and a characteristic decomposition of the two dimensional compressible Euler equations, Comm. Math. Phys., 267, 1-12 (2006) · Zbl 1113.76080
[11] Zafar, M.; Sharma, VD, Characteristic decomposition of compressible Euler equations for a non-ideal gas in two-dimensions, J. Math. Phys., 55, 9, 1-12 (2014) · Zbl 1366.35148
[12] Zafar, M., A note on characteristic decomposition for two-dimensional Euler system in van der Waals fluids, Int. J. Nonlin. Mech., 86, 33-36 (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.