Abstract
A convergence theorem of the fractional step Lax-Friedrichs scheme and Godunov scheme for an inhomogeneous system of isentropic gas dynamics (1<γ≦5/3) is established by using the framework of compensated compactness. Meanwhile, a corresponding existence theorem of global solutions with large data containing the vacuum is obtained.
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Communicated by A. Jaffe
Partially supported by U.S. NSF Grant # DMS-850403
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Xiaxi, D., Gui-Qiang, C. & Peizhu, L. Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics. Commun.Math. Phys. 121, 63–84 (1989). https://doi.org/10.1007/BF01218624
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DOI: https://doi.org/10.1007/BF01218624