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Global Continuous Sonic–Supersonic Flows in Two-Dimensional Semi-infinite Divergent Ducts

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Abstract

We study the existence of global continuous sonic–supersonic flows in a two-dimensional semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the duct, and the state of the flow is sonic at the inlet of the duct. One of the main difficulties for the global existence is that the 2D steady Euler system becomes degenerate at the inlet of the duct. To overcome this difficulty, we establish some uniform interior \(C^{0, 1}\) estimates for the global supersonic solutions to a sequence of regularized problems, and then use the Arzela–Ascoli theorem and a standard diagonal procedure to construct a global continuous sonic–supersonic solution in the duct. Sufficient conditions for the existence or nonexistence of vacuum in the duct are also given.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Geng Lai

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  1. Geng Lai
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Correspondence to Geng Lai.

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Communicated by T. Nishida

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This work is partially supported by NSFC 12071278.

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Lai, G. Global Continuous Sonic–Supersonic Flows in Two-Dimensional Semi-infinite Divergent Ducts. J. Math. Fluid Mech. 23, 77 (2021). https://doi.org/10.1007/s00021-021-00601-2

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