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The Existence of Steady Compressible Subsonic Impinging Jet Flows

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Abstract

In this paper, we investigate the compressible subsonic impinging jet flows through a semi-infinitely long nozzle and impacting on a solid wall. Firstly, it is shown that given a two-dimensional semi-infinitely long nozzle and a wall behind the nozzle, and an appropriate atmospheric pressure, then there exists a smooth global subsonic compressible impinging jet flow with two asymptotic directions. The subsonic impinging jet develops two free streamlines, which initiate smoothly at the end points of the semi-infinitely long nozzles. In particular, there exists a smooth curve which separates the fluids which go to different places downstream. Moreover, under some suitable asymptotic assumptions of the nozzle, the asymptotic behaviors of the compressible subsonic impinging jet flows in the inlet and the downstream are obtained by means of a blow-up argument. On the other hand, the non-existence of compressible subsonic impinging jet flows with only one asymptotic direction is also established. This main result in this paper solves the open problem (4) in Chapter 16.3 proposed by Friedman in his famous survey (Friedman in Mathematics in industrial problems, II, I.M.A. volumes in mathematics and its applications, vol 24, Springer, New York, 1989).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

    Jianfeng Cheng & Lili Du

  2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Yongfu Wang

Authors
  1. Jianfeng Cheng
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  2. Lili Du
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  3. Yongfu Wang
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Correspondence to Lili Du.

Additional information

Communicated by P. Rabinowitz

Cheng is supported by the Fundamental Research Funds for the Central Universities 2012017yjsy107. Du is supported in part by NSFC Grant 11571243, 11622105 and PCSIRT (IRT_16R53) from the Chinese Education Ministry. Wang is supported by the Fundamental Research Funds for the Central Universities 221410004005040132.

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Cheng, J., Du, L. & Wang, Y. The Existence of Steady Compressible Subsonic Impinging Jet Flows. Arch Rational Mech Anal 229, 953–1014 (2018). https://doi.org/10.1007/s00205-018-1230-8

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  • DOI: https://doi.org/10.1007/s00205-018-1230-8

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