ON THE WEAK DISCONTINUITY SURFACES AND TAPES OF EQUATION SYSTEMS IN FLUID MECHANICS

The weak discontinuity surfaces for a system of quasi-linear differential equations of higher order are developed.The classification of equation systems in fluid mechanics is based on the propagative weak discontinuity surfaces.Types of equations for different flow models are discussed.The conclusion is as follows:(a) For incompressible nonviscous flow,incompressible viscous flow and compressible viscous flow,the types of equations are all parabolic in the unsteady case and elliptic in the steady case.(b) For compressible nonviscous flow,the type of equations is hyperbolic in the unsteady case or steady supersonic case,and the type is elliptic in the steady subsonic case.     

Large time behaviors of the isentropic bipolar compressible Navier-Stokes-Poisson system

The isentropic bipolar compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l(R3) ∩ B˙ s 1,1 (R3) with l ≥ 4 and s ∈ (0, 1], it is shown that the momenta of the charged particles decay at the optimal rate (1+t) 1 4 s 2 in L2 -norm, which is slower than the rate (1+t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both (1 + t) 3 4 due to the cancellation effect from the interplay interaction of the charged particles.     

Time-Periodic Solution to the Compressible Navier–Stokes/Allen–Cahn System

In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.     

A Remark on Global Existence in H^4 for a Nonlinear Thermoviscoelasticity Equations with Non-monotone Pressure

We consider a one-dimensional continuous model of nutron star,described by a compressible thermoviscoelastic system with a non-monotone equation of state,due to the effective Skyrme nuclear interaction between particles.We will prove that,despite a possible, destabilizing influence of the pressure,which is non-monotone and not always positive,the presence of viscosity and a sufficient thermal dissipation dcscribc the global existence of solutions in H~4 with a mixed free boundary problem for our model.     

Preface: Hyperbolic System of Conservation Laws and Related Topics

<正>The history of hyperbolic system of conservation laws can date back to the eighteenth century, after several works of the natural philosophers, most notably L. Euler. The compressible Euler system, consisting of mass, momentum and energy in the divergence form, is the prototypical model of the hyperbolic system of conservation laws, and its main feature is the shock formation in a finite time no matter how the initial values smooth. This poses huge challenges in the mathematical analysi...     

Stability of weak solutions for the compressible Navier-Stokes-Poisson equations

In this paper, we consider the isentropic compressible Navier-Stokes-Poisson equations arising from transport of charged particles or motion of gaseous stars in astrophysics. We are interested in the case that the viscosity coefficients depend on the density and shall degenerate in the appearance of (density) vacuum, and show the L 1 -stability of weak solutions for arbitrarily large data on spatial multi-dimensional bounded or periodic domain or whole space.     

BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L~∞(0, T; L~6)-norm of the density of particles and the L~1(0, T; L~∞)-norm of the deformation tensor of velocity gradient.     

COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R~3

The compressible non-isentropic bipolar Navier-Stokes-Poisson (BNSP) system is investigated in R 3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in H l (R 3 ) ∩ Bs 1,1 (R 3 ) for l ≥ 4 and s ∈ (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t) 3 4 , but the momentum for each particle decays at the optimal rate (1 + t) 1 4 s 2 which is slower than the rate (1 + t) 3 4 s 2 for the compressible Navier-Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1+t) 3 4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.     

ON GLOBAL BEHAVIOR OF WEAK SOLUTIONS OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS

In this article,we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces.By adapting the arguments for the compressible Navier-Stokes equations,and carefully analyzing the direction field of liquid crystals in the equations of angular momentum,we show the existence of bounded absorbing sets,global bounded trajectories,and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ5/3.     

Navier-Stokes/Allen-Cahn System with Generalized Navier Boundary Condition

In this paper, we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations. The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation. The existence and uniqueness for local strong solution in three dimensional bounded domain for this type o...     

Particules collantes signées et lois de conservation scalaires 1DSigned sticky particles and 1D scalar conservation laws

We present an approximation of the entropy solution of a 1D scalar conservation law based on signed sticky particles when the variation of the initial condition is bounded. This method is a generalization of the one studied by Brenier and Grenier [2] in case the initial condition is monotone. When they collide, particles with the same sign stick together with conservation of the momentum whereas particles with opposite sign are destroyed. We prove the convergence of the approximate solution to the entropy solution when the initial number of particles goes to +∞. To cite this article: B. Jourdain, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 233–238.     

NEW METHOD FOR EFFECTIVE VISCOSITY OF COLLOIDAL DISPERSIONS WITH PERIODIC MICROSTRUCTURES

1IntroductionTherheologyofcolloidaldispersionisofinterestinmanyphsicalandtechnologicalproblems,andforthisreasonithasbeenstudiedextensively,expeciallywhenthesystemcallI)edescribedbythelillearNavier-StokesequationsforincompressibleNewtonianfiuicl[1--6J.ColIoidaldispersioncanbesubdividedintotwoclasses,namely,suspensionandemulsi.I,[7'8].Asuspensionisadispersionwithfinerigidparticlessuspendedinafluid.Inanemulsion,pallidparticlesareimmersedinanotherfluid.Animportantprobleminthisfieldistodeters-f…     

L'effet Hawking pour un champ de DiracThe Hawking effect for the Dirac field

We consider the gravitational collapse of the charged star leading to a black-hole. We prove that a fixed observer in Schwarzschild variables observes, at the last moments of the collapse in his own proper time, an outgoing thermal flux of spin 1/2 particles containing preferentially the particles with the same charge that the black-hole. This is the Hawking effect. To cite this article: F. Melnyk, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 643–648.     

Dérivation de modèles couplés dérive-diffusion/cinétique par une méthode de décomposition en vitesseDerivation of a kinetic/drift-diffusion model describing fast and slow particles

Our purpose is to derive a model describing the evolution of charged particles in a plasma, at various scales following their kinetic energy. Fast particles will be described through a collisional kinetic equation of Boltzmann type. This equation will be coupled with a drift-diffusion model that describes the evolution of slower particles. The main interest of this approach is to reduce the cost of numerical simulations. This gain is due to the use of a macroscopic model for slow particles instead of a kinetic model for all the particles, which would involve a larger number of variables. To cite this article: N. Crouseilles, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 827–832.     

关于“预拓扑与网族的预收敛类”的注

本文研究了预拓扑空间中的收敛问题.利用完备格同构的方法,获得了预拓扑与预收敛类可以相互确定的结果,推广了拓扑与收敛类可以相互确定的结果,同时推广了文献[1]的结果.     

非线性约束优化问题的混合粒子群算法

把处理约束条件的一个外点方法和改进的粒子群优化算法相结合,提出了一种求解非线性约束优化问题的混合粒子群优化算法.该方法兼顾了粒子群优化和外点法的优点,对算法迭代过程中出现不可行粒子,利用外点法处理后产生可行粒子.数值实验表明了提出的新算法具有有效性、通用性和稳健性.     

球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。     

量子群中的Coxeter变换的“阶”

设g是有限维复单李代数。本文考虑量子群U_q(g)中两个特殊的自同构及它们作用在U_q(g)上及其可积U_q(g)-模上的性态。     

量子群中的Coxeter变换的"阶"

设g是有限维复单李代数.本文考虑量子群Uq(g)中两个特殊的自同构及它们作用在Uq(g)上及其可积Uq(g)-模上的性态.     

NONCOALESCENCE OF BROWNIAN MOTION REFLECTING ON A SPHERE*

In this paper, we will show that two particles starting from different positions and driven by the same Brownian motion reflecting normally on a sphere will never meet. If their initial positions are inside a ball, they will hit the boundary simultaneously in a finite time.