STABILIZATION EFFECT OF FRICTIONS FOR TRANSONIC SHOCKS IN STEADY COMPRESSIBLE EULER FLOWS PASSING THREE-DIMENSIONAL DUCTS  

作　　者：Hairong YUAN Qin ZHAO 袁海荣;赵勤(School of Mathematical Sciences,and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,East China Normal University,Shanghai 200241,China;Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]School of Mathematical Sciences,and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,East China Normal University,Shanghai 200241,China [2]Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070,China

出　　处：《Acta Mathematica Scientia》2020年第2期470-502,共33页数学物理学报（B辑英文版）

基　　金：This work was supported in part by National Nature Science Foundation of China(11371141 and 11871218);by Science and Technology Commission of Shanghai Municipality(18dz2271000).

摘　　要：Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets.For the three-dimensional steady non-isentropic compressible Euler system with frictions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections.In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces.This manifests that frictions have a stabilization effect on transonic shocks in ducts,in consideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts.Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.

关 键 词：Stability transonic shocks Fanno flow THREE-DIMENSIONAL Euler system FRICTIONS decomposition nonlocal elliptic problem Venttsel boundary condition elliptic-hyperbolic mixed-composite tpe 

分 类 号：O175[理学—数学]