Abstract
We present a characteristic decomposition of the potential flow equation in the self-similar plane. The decomposition allows for a proof that any wave adjacent to a constant state is a simple wave for the adiabatic Euler system. This result is a generalization of the well-known result on 2-d steady potential flow and a recent similar result on the pressure gradient system.
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References
Čanić S., Keyfitz B.L. (1998) Quasi-one-dimensional Riemann problems and their role in self-similar two-dimensional problems. Arch. Rat. Mech. Anal. 144, 233–258
Courant R., Friedrichs K.O. (1948) Supersonic flow and shock waves. Interscience, New York
Dafermos C. (2000) Hyperbolic conservation laws in continuum physics (Grundlehren der mathematischen Wissenschaften). Springer, Berlin Heidelberg New York, pp. 443
Dai Zihuan, Zhang Tong (2000) Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics. Arch. Rational Mech. Anal. 155, 277–298
Lax P. (1964) Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5, 611–613
Li, Jiequan (2001) On the two-dimensional gas expansion for compressible Euler equations. SIAM J. Appl. Math. 62, 831–852
Li, Jiequan; Zhang, Tong; Yang, Shuli The two-dimensional Riemann problem in gas dynamics. Pitman monographs and surveys in pure and applied mathematics 98. London-NewYork: Addison Wesley Longman limited, 1998
Zhang Tong, Zheng Yuxi (1990) Conjecture on the structure of solution of the Riemann problem for two-dimensional gas dynamics systems. SIAM J. Math. Anal. 21, 593–630
Zheng, Yuxi (2001) Systems of conservation laws: Two-dimensional Riemann problems 38 PNLDE. Birkhäuser, Boston
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Communicated by P. Constantin
Research partially supported by NSF of China with No. 10301022, NSF from Beijing Municipality, Fok Ying Tong Educational Foundation, and the Key Program from Beijing Educational Commission with no. KZ200510028018.
Research partially supported by NSF-DMS-0305497, 0305114.
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Li, J., Zhang, T. & Zheng, Y. Simple Waves and a Characteristic Decomposition of the Two Dimensional Compressible Euler Equations. Commun. Math. Phys. 267, 1–12 (2006). https://doi.org/10.1007/s00220-006-0033-1
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DOI: https://doi.org/10.1007/s00220-006-0033-1