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On a Degenerate Free Boundary Problem and Continuous Subsonic–Sonic Flows in a Convergent Nozzle

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Abstract

This paper concerns the well-posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary. Such problems arise when studying continuous subsonic–sonic flows in a convergent nozzle with straight solid walls. It is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic–sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux. Furthermore, the sonic curve of this continuous subsonic–sonic flow is a free boundary, where the flow is singular in the sense that while the speed is C 1/2 Hölder continuous at the sonic state, the acceleration blows up at the sonic state.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Chunpeng Wang

  2. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Chunpeng Wang & Zhouping Xin

Authors
  1. Chunpeng Wang
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  2. Zhouping Xin
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Correspondence to Zhouping Xin.

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Communicated by A. Bressan

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Wang, C., Xin, Z. On a Degenerate Free Boundary Problem and Continuous Subsonic–Sonic Flows in a Convergent Nozzle. Arch Rational Mech Anal 208, 911–975 (2013). https://doi.org/10.1007/s00205-012-0607-3

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  • DOI: https://doi.org/10.1007/s00205-012-0607-3

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