Communications in Mathematical Physics

, Volume 83, Issue 2, pp 243–260 | Cite as

Nonlinear stability and instability of transonic flows through a nozzle

  • T.-P. Liu


We study transonic flows along a nozzle based on a one-dimensional model. It is shown that flows along the expanding portion of the nozzle are stable. On the other hand, flows with standing shock waves along a contracting duct are dynamically unstable. This was conjectured by the author based on the study of noninteracting wave patterns. The author had shown earlier that supersonic and subsonic flows along a duct with various cross sections are stable. Basic to our analysis are estimates showing that shock waves tend to decelerate along an expanding duct and accelerate along a contracting duct.


Neural Network Statistical Physic Shock Wave Complex System Nonlinear Dynamics 


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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • T.-P. Liu
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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