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| Structural Stability of 3D Axisymmetric Steady Subsonic Euler Flows inFinitely Long Nozzles with Variable End Pressures |
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Citation： |
Jun LI,Yannan WANG.Structural Stability of 3D Axisymmetric Steady Subsonic Euler Flows inFinitely Long Nozzles with Variable End Pressures[J].Chinese Annals of Mathematics B,2025,46(4):481~520 |
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Net amount： 6 |
Authors： |
Jun LI; Yannan WANG |
Foundation： |
the National Key Research and Development Program of China
(No. 2024YFA1013301). |
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| Abstract： |
As a continuation of [Li; J. and Wang; Y. N.; Structural stability of steady
subsonic Euler flows in 2D finitely long nozzles with variable end pressure; J. Differential
Equations; 413; 2014; 70–109]; in this paper; the authors study the structural stability of
three dimensional axisymmetric steady subsonic Euler flows in finitely long curved nozzles.
The reference flow is a general subsonic shear flow in a three dimensional regular cylindrical nozzle with general size of vorticity and without stagnation points. The problem is
described by the well-known steady compressible Euler system. With a class of admissible physical conditions and prescribed pressure at the entrance and the exit of the nozzle
respectively; they establish the structural stability of this kind of axisymmetric subsonic
shear flow with no-zero swirl velocity. Due to the hyperbolic-elliptic coupled form of the
Euler system in subsonic regions; the problem is reformulated via a twofold normalized process; including straightening the lateral boundary of the nozzle under the natural Cartesian
coordinates and reformulating the problem under the cylindrical coordinates. Accordingly;
the Euler system is decoupled into an elliptic mode and three hyperbolic modes with some
artificial singular terms under the cylindrical coordinates. The elliptic mode is a mixed
type boundary value problem of first order elliptic system for the pressure and the radial
velocity angle. Meanwhile; the hyperbolic modes are transport type to control the total
energy; the specific entropy and the swirl velocity; respectively. The estimates as well as
well-posedness are executed in a Banach space with optimal regularity under the natural
Cartesian coordinates in place of the cylindrical coordinates. The authors develop a systematic framework to deal with the artificial singularity and the non-zero swirl velocity in
three dimensional axisymmetric case. Their strategy is helpful for other three dimensional
problems under axisymmetry. |
Keywords： |
Steady compressible Euler system Subsonic shear flow First order
elliptic system Structural stability Axisymmetry |
Classification： |
Steady compressible Euler system; Subsonic shear flow; First order
elliptic system; Structural stability; Axisymmetry |
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