Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 219-237.

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Well-Posedness and Convergence Rates of Three-Dimensional Incompressible Euler Flows in Axisymmetric Nozzles with Symmetric Body

Jie Lin(),Tianyi Wang*()   

  1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070
  • Received:2022-05-13 Revised:2022-08-05 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The NSFC(11971307)


This paper studies the three-dimensional incompressible Euler flows in axisymmetric nozzles with a symmetric body. The well-posedness is established by stream function method and barrier function. Base on the above well-posedness, the far field convergence rates of the solutions are studied: if the infinite nozzles are the flat boundary outside the finite length, the solution of the equation converges to an asymptotic state at the exponential rate; if the infinite nozzles converge to the flat boundary with the polynomial rates, the solutions converge to the asymptotic states at the same polynomial rates.

Key words: Incompressible Euler equations, Axisymmetric Nozzles, Well-posedness, Convergence rates

CLC Number: 

  • O175.2