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STABILIZATION EFFECT OF FRICTIONS FOR transonic shocks IN STEADY COMPRESSIBLE EULER FLOWS PASSING THREE-DIMENSIONAL DUCTS

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Acta Mathematica Scientia 2020年第2期40卷 470-502页

作者：袁海荣赵勤 School of Mathematical Sciences and Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200241China Department of Mathematics School of ScienceWuhan University of TechnologyWuhan 430070China

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

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Two-Dimensional Riemann Problems:transonic Shock Waves and Free Boundary Problems

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1015-1052页

作者： Gui-Qiang G.Chen Oxford Centre for Nonlinear PDE Mathematical InstituteUniversity of OxfordOxford OX26GGUK

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

关键词： Riemann problems Two-dimensional(2-D) transonic shocks Solution structure Free boundary problems Mixed elliptic-hyperbolic type Global configurations Large-time asymptotics Global attractors Multidimensional(M-D) Shock capturing methods

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transonic SHOCK SOLUTIONS TO THE EULER SYSTEM IN DIVERGENT-CONVERGENT NOZZLES

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Acta Mathematica Scientia 2022年第4期42卷 1536-1546页

作者：段犇兰傲罗珍 School of Mathematical Sciences Jilin UniversityChangchun 130012 China School of Mathematics Dalian University of TechnologyDalian116024China School of Mathematical Sciences Xiamen UniversityXiamen 361005China

In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.

关键词： Euler system transonic shocks steady solutions nozzle

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