Abstract.

In this paper, the low Mach number limit and far field convergence rates are investigated for steady irrotational flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, with the aid of uniform a priori estimates, we proved the well-posedness theory for both incompressible flows and compressible subsonic flows with external forces in a multidimensional nozzle with an obstacle inside. Furthermore, the uniformly subsonic compressible flows tend to the incompressible flows with quadratic order of Mach numbers as the compressibility parameter goes to zero. We finally give the convergence rates of both incompressible and compressible flows at far fields as the boundary of the nozzle goes to flat even when the forces do not admit convergence rates at far fields. These results reveal how the external forces affect the convergence rates of the flows at far fields.

Keywords

  1. subsonic flows
  2. irrotational flows
  3. nozzles
  4. external forces
  5. low Mach number limit
  6. convergence rates

MSC codes

  1. 35J25
  2. 35B25
  3. 35B40
  4. 76G25
  5. 76N10

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Acknowledgment.

The authors thank the referees for their helpful comments, which help improve the presentation of the paper.

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 36 - 67
ISSN (online): 1095-7154

History

Submitted: 20 January 2022
Accepted: 22 September 2022
Published online: 24 January 2023

Keywords

  1. subsonic flows
  2. irrotational flows
  3. nozzles
  4. external forces
  5. low Mach number limit
  6. convergence rates

MSC codes

  1. 35J25
  2. 35B25
  3. 35B40
  4. 76G25
  5. 76N10

Authors

Affiliations

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China.
Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan, Hubei 430070, China.
School of Mathematical Sciences, Institute of Natural Sciences, Ministry of Education Key Laboratory of Scientific and Engineering Computing, and CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China.

Funding Information

Funding: The research of the second author was supported in part by NSFC grants 11601401 and 11971024. The research of the third author was partially supported by NSFC grants 11971307 and 11631008, Natural Science Foundation of Shanghai grant 21ZR1433300, and Shanghai Science and Technology Commission grant 22XD1421400.

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