Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (6): 2131-2140.doi: 10.1016/S0252-9602(11)60389-5

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ON MULTI-DIMENSIONAL SONIC-SUBSONIC FLOW

 HUANG Fei-Min, WANG Tian-Yi, WANG Yong   

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China
  • Received:2011-05-04 Online:2011-11-20 Published:2011-11-20
  • Supported by:

    The research of FMH was supported in part by NSFC (10825102) for distinguished youth scholar, and National Basic Research Program of China (973 Program) under Grant No. 2011CB808002.

Abstract:

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the n-dimensional (n ≥ 2) Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy H−1 loc (Ω) com-pactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional (n ≥ 2) Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension (n ≥ 3).

Key words: multi-dimension, sonic-subsonic flow, steady irrotational flow, compensated compactness

CLC Number: 

  • 35L65
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