GLOBAL ENTROPY SOLUTIONS TO AN INHOMOGENEOUS ISENTROPIC COMPRESSIBLE EULER SYSTEM

In this article, we develop a new technique to prove the global existene of entropy solutions to an inhomogeneous isentropic compressible Euler equations through the compensated compactness and vanishing viscosity method. In particular, the entropy solutions are uniformly bounded independent of time.     

关于一类非线性双曲方程组的二维Cauchy问题

本文通过引进新的广义解定义，对一类非线性双曲方程组的二维Ｃａｕｃｈｙ问题，证明了解的存在唯一性．并且，解可能含δ波．     

一类双曲守恒律方程组的二维Riemann问题

本文中，我们构造了一类非线性双曲守恒律的二维Ｒｉｅｍａｎｎ问题的整体解。     

Euler-Possion 半导体模型的大时间行为

本文研究了Euler-Poisson半导体模型弱熵解的大时间行为, 得到了一致有界的弱熵解随着时间t指数衰减到稳态解. 本文的结果不需要假定解是``小"的, 也不需要假定解的正则性.     

ON THE CAUCHY PROBLEM OF TRANSPORTATION EQUATIONS

1.IntroductionInthepreselltpaper,weconsiderthetransportationsystemwithinitialdatawherepanduaredensityandvelocityrespectively.Thesystemofconservationlaws(1.1)describesthefluidmechanicswithconstalltpressuxe,whichisusedinplasmaphysicswherepressureisassumedtobeaconstant.Thissystemisnon--strictlyhyperbolicwithadoubleeigenvalueAl~AZ=albothAl,AZbeinglinearlydegenerate.AndtheCauchyproblemforthissystemisnotwell-posedintheclassofmeasurableandboundedfunctions(see[3]).Inthepresentpaper,weintroduceanew…     

ON MULTI-DIMENSIONAL SONIC-SUBSONIC FLOW

In this paper, a compensated compactness framework is established for sonicsubsonic approximate solutions to the n-dimensional (n ≥ 2) Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy H 1 loc (Ω) compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional (n ≥ 2) Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension (n ≥ 3).     

Stability of viscous contact wave for compressible navier-stokes system of general gas with free boundary

In this paper, we study the large time behavior of solutions to the nonisentropic Navier-Stokes equations of general gas, where polytropic gas is included as a special case, with a free boundary. First we construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation, in finite time as the heat conductivity tends to zero. Then we prove the viscous contact wave is asymptotic stable if the initial perturbations and the strength of the contact wave are small. This generalizes our previous result [6] which is only for polytropic gas.     

UNIQUENESS ON ZERO PRESSURE GAS DYNAMICS

In this papert we study a 2 x 2 hyperbolic systenlwhere p 2 0 and u are density al1d velocity of gases, respective1y.The systen1 of conservatiou laws (1) is called pressureless fiow or pressureless gases. Itis forlllally obtailled by letting pressure to zero ill tl1e compressible Euler equations. It is alsoknown as sticky particle model in astrophysics (see [21] ).Olle Of the main difficulties for the mathematical analysis of (1) is that the solution is lloll-negative llleasurel uot function.…     

关于等温气流的逼近解的收敛性

该文研究等温气流整体解的存在性．我们用补偿列紧理论证明了逼近解的强收敛性．我们不仅对弱熵,而且对强熵也建立了交换关系式．在证明中我们不需要强熵的Ｈ－１紧性．     

SOLUTIONS CONTAINING DELTA－WAVES OF CAUCHY PROBLEMS FOR A NONSTRICTLY HYPERBOLIC SYSTEM

ＳＯＬＵＴＩＯＮＳＣＯＮＴＡＩＮＩＮＧＤＥＬＴＡ－ＷＡＶＥＳＯＦＣＡＵＣＨＹＰＲＯＢＬＥＭＳＦＯＲＡＮＯＮＳＴＲＩＣＴＬＹＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭ￥ＨＵＡＮＧＦＥＩＭＩＮ（黄飞敏）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ,Ｓｈａｎｔｏｕ...