Transonic shocks for 3-D axisymmetric compressible inviscid flows in cylinders

Park, Hyangdong; Ryu, Hyeongyu

doi:10.1016/j.jde.2020.06.016

Cited by 5 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See also, for instance, [10,31] and references therein for literatures on quasi-one-dimensional nozzle flows. As to the steady multi-dimensional models such as potential equations or the Euler system, thanks to continuous efforts of many mathematicians, there have been substantial progresses in the past two decades, for instance, see [1,2,3,4,5,6,7,8,9,11,15,16,17,20,21,22,23,24,25,27,28,32,33,34,35,36,37,38,39,40,41]. Two typical kinds of nozzles are studied.…”

Section: Letmentioning

confidence: 99%

On Admissible Positions of Transonic Shocks for Steady Isothermal Euler Flows in a Horizontal Flat Nozzle under Vertical Gravity

Fang¹,

Gao²

2021

Preprint

View full text Add to dashboard Cite

The small perturbation problem 6 1.3. Outline of the paper. 12 2. The Lagrange transformation and the main results 13 2.1. Reformulation by the Lagrange transformation. 13 2.2. The free boundary problem for the initial approximation. 18 2.3. Main results 20 3. A preliminary: boundary value problems of a typical elliptic-hyperbolic composite system 23 4. The initial approximation 27 4.1. The solution U− in Ω 27 4.2. Reformulation of the linearized R-H conditions (2.61)-(2.62). 29 4.3. Determine ξ * and U+ . 31 5. The nonlinear iteration scheme 35 5.1. The supersonic flow U − in Ω 35 5.2. The shock front and subsonic flow 37 5.3. The linearized problem for the iteration 38 5.4. The solvability condition and a prior estimates of δU * 41 6. Well-posedness and contractiveness of the iteration scheme 42 Acknowlegements 50 References 50

show abstract