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| 1 | Riemann boundary value problems and reflection of shock for the Chaplygin gas显示文摘In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp. | CHEN ShuXing 1,& QU AiFang 2 1 School of Mathematical Sciences,Fudan University,Shanghai 200433,China 2 Wuhan Institute of Physics and Mathematics,Chinese Academy of Sciences,Wuhan 430071,China | 2012 | Science China Mathematics2012，55，4： | 6 |
| 2 | Protective effect of a DNA vaccine delivered in attenuated Salmonella typhimurium against Toxoplasma gondii infection in mice显示文摘 | Daofeng Qu Suhua Wang Weiming Cai Aifang Du | 2008 | Vaccine2008，，： | 1 |
| 3 | Piston Problems of Two-Dimensional Chaplygin Gas显示文摘In this paper,the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas.The angle of the piston is allowed to vary in a wide range.The piston can be pushed forward into the static gas,or pulled back from the gas.The global existence of solution to the piston problem with any initial speed is established,and the structures of the global solutions are clearly described.The authors find that for the proceeding piston problem the front shock can be detached,attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston;while for the receding problem the front rarefaction wave is always detached and the concentration will never occur. | Shuxing CHEN Aifang QU | 2019 | Chinese Annals of Mathematics,Series B2019，40，6： | 0 |
| 4 | Steady Compressible Euler Equations of Concentration Layers for Hypersonic-limit Flows Passing Three-dimensional Bodies and Generalized Newton-Busemann Pressure Law显示文摘For stationary hypersonic-limit Euler flows passing a solid body in three-dimensional space,the shock-front coincides with the upwind surface of the body,hence there is an infinite-thin layer of concentrated mass,in which all particles hitting the body move along its upwind surface.By proposing a concept of Radon measure solutions of boundary value problems of the multi-dimensional compressible Euler equations,which incorporates the large-scale of three-dimensional distributions of upcoming hypersonic flows and the small-scale of particles moving on two-dimensional surfaces,the authors derive the compressible Euler equations for flows in concentration layers,which is a stationary pressureless compressible Euler system with source terms and independent variables on curved surface.As a by-product,they obtain a formula for pressure distribution on surfaces of general obstacles in hypersonic flows,which is a generalization of the classical Newton-Busemann law for drag/lift in hypersonic aerodynamics. | Aifang QU Hairong YUAN | 2023 | Chinese Annals of Mathematics,Series B2023，44，4： | 0 |
| 5 | Radon Measure Solutions to Riemann Problems for Isentropic Compressible Euler Equations of Polytropic Gases显示文摘We solve the Riemann problems for isentropic compressible Euler equations of polytropic gases in the class of Radon measures,and the solutions admit the concentration of mass.It is found that under the requirement of satisfying the over-compressing entropy condition:(i)there is a unique delta shock solution,corresponding to the case that has two strong classical Lax shocks;(ii)for the initial data that the classical Riemann solution contains a shock wave and a rarefaction wave,or two shocks with one being weak,there are infinitely many solutions,each consists of a delta shock and a rarefaction wave;(iii)there are no delta shocks for the case that the classical entropy weak solutions consist only of rarefaction waves.These solutions are self-similar.Furthermore,for the generalized Riemann problem with mass concentrated initially at the discontinuous point of initial data,there always exists a unique delta shock for at least a short time.It could be prolonged to a global solution.Not all the solutions are self-similar due to the initial velocity of the concentrated point-mass(particle).Whether the delta shock solutions constructed satisfy the over-compressing entropy condition is clarified.This is the first result on the construction of singular measure solutions to the compressible Euler system of polytropic gases,that is strictly hyperbolic,and whose characteristics are both genuinely nonlinear.We also discuss possible physical interpretations and applications of these new solutions. | Yunjuan Jin Aifang Qu Hairong Yuan | 2023 | Communications on Applied Mathematics and Computation2023，5，3： | 0 |
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