Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system

We investigate the zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system.We justify this singular limit rigorously in the framework of smooth solutions and obtain the nonisentropic compressible magnetohydrodynamic equations as the dielectric constant tends to zero.     

Lie symmetries of a system arising in plasma physics

Lie group classification for a diffusion‐type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. Certain initial value problems are reduced to problems with the governing equations being ordinary differential equations. Examples of potential symmetries are also presented.     

Quasineutral limit of an euler-poisson system arising from plasma physics

In this paper, we study the quasineutral limit of an Euler-Poisson system arising from plasma physics i.e. the limit when the Debye length tends to of a non linear hyperbolic system coupled with a non linear elliptic equation.The proof uses pseudodiiferential energy estimates techniques, in order to justify classical limits in small time, for strong solutions.     

Asymptotic stability for one-dimensional motion of non-Newtonian compressible fluids

Rarefaction wave solutions for a one-dimensional model system associated with nomNewtonian compressible fluid are investigated in terms of asymptotic stability. The rarefaction wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small. The proof is given by the elemental L2 energy method.     

Stability of stationary solutions for the non-isentropic Euler-Maxwell system in the whole space

In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R³. It is known in the authors’ previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method.     

Anomalous transport of particles in plasma physics

We investigate the long time/small mean-free-path asymptotic behavior of the solutions of a Vlasov–Lévy–Fokker–Planck equation and show that the asymptotic dynamics for the VLFP are described by an anomalous diffusion equation.     

Asymptotic behavior of self-normalized trimmed sums: Nonnormal limits II

Let {X _j} be independent, identically distributed random variables which are symmetric about the origin and have a continuous nondegenerate distributionF. Let {X _n(1),...,X _n(n)} denote the arrangement of {X ₁,...,X _n} in decreasing order of magnitude, so that with probability one, |X _n(1)|>|X _n(2)|>...> |X _n(n)|. For initegersr _n such thatr _n/n0, define the self-normalized trimmed sumT _n= _i=rn ⁿ X _n(i)/{ _i=rn ⁿ X _n ² (i)}^1/2. Hahn and Weiner⁽⁶⁾ showed that under a probabilistically meaningful analytic condition generalizing the asymptotic normality criterion forT _n, various nonnormal limit laws forT _n arise which are represented by means of infinite random series. The analytic condition is now extended and the previous approach is refined to obtain limits which are mixtures of a normal, a Rademacher, and a law represented by a more general random series. Each such limit law actually arises as can be seen from the construction of a single distribution whose correspondingL(T _n ) generates all of the law along different subsequences, at least if {r _n} grows sufficiency fast. Another example clarifies the limitations of the basic approach.     

Asymptotic stability of periodic solution for compressible viscous van der Waals fluids

This paper is concerned with the asymptotic stability of the periodic solution to a one-dimensional model system for the compressible viscous van der Waals fluid in Eulerian coordinates. If the initial density and initial momentum are suitably close to the average density and average momentum, then the solution is proved to tend toward a stationary solution as t -→∞.     

Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space

In the present paper, we investigate the large-time behavior of the solution to an initial-boundary value problem for the isentropic compressible Navier-Stokes equations in the Eulerian coordinate in the half space. This is one of the series of papers by the authors on the stability of nonlinear waves for the outflow problem of the compressible Navier-Stokes equations. Some suitable assumptions are made to guarantee that the time-asymptotic state is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Employing the L²-energy method and making use of the techniques from the paper [S. Kawashima, Y. Nikkuni, Stability of rarefaction waves for the discrete Boltzmann equations, Adv. Math. Sci. Appl. 12 (1) (2002) 327-353], we prove that this nonlinear wave is nonlinearly stable under a small perturbation. The complexity of nonlinear wave leads to many complicated terms in the course of establishing the a priori estimates, however those terms are of two basic types, and the terms of each type are “good” and can be evaluated suitably by using the decay (in both time and space variables) estimates of each component of nonlinear wave.     

Asymptotic limits of a self-dual Ginzburg–Landau functional in bounded domains

In the author's joint paper [HJS] with Jost and Struwe, we discuss asymtotic limits of a self-dual Ginzburg–Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains. Received: 20 June 1997     

Asymptotic behaviour of solutions to the Navier-Stokes equations of a two-dimensional compressible flow

In this paper,we are concerned with the asymptotic behaviour of a weak solution to the Navier-Stokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(e) = a log d(e) for large .Here d > 2,a > 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.     

Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum

The asymptotic behavior of solutions of the damped compressible Euler equations is conjectured to obey to the famous porous media equations (PMES). The previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic. In present paper, we prove that the L^∞ entropy weak solution with vacuum, obtained by the compensated compactness theory, converges strongly in space to the unique similarity solution of the related PME, as time goes to infinity.     

Global relaxation and nonrelativistic limit of nonisentropic Euler-Maxwell systems

The aim of this paper is to investigate smooth solutions to Cauchy (or periodic) problem for a nonisentropic Euler-Maxwell system with small parameters. For initial data close to constant equilibrium states, we prove the global-in-time convergence of the Euler-Maxwell system as parameters go to zero. The limit systems are the drift-diffusion system and the nonisentropic Euler-Poisson system, respectively.     

Fusion modeling in plasma physics: Vlasov-like systems

The methods developed by authors are applied to some reductions of BBGKY hierarchy, namely, various examples of Vlasovlike systems which are important both for fusion modeling and for particular physical problems related to plasma/beam physics. We mostly concentrate on phenomena of localization and pattern formation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Condensation of charged bosons in plasma physics and cosmology

We consider the screening of impurities in plasma with a Bose-Einstein condensate of electrically charged bosons and show that the screened potential is drastically different from the usual Debye potential. The polarization operator of photons in plasma acquires infrared singular terms at small photon momentum, and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Friedel oscillations in plasma with degenerate fermions. We also discuss the magnetic properties of the cosmological plasma with condensed W bosons and show that W bosons condense in the ferromagnetic state. This could lead to spontaneous magnetization of the primeval plasma. The created magnetic fields may seed galactic and intergalactic magnetic fields observed in the present-day Universe.     

Rayleigh-Taylor instability of a compressible plasma in a horizontal magnetic field

A study of the Rayleigh instability of a compressible plasma, density stratified in horizontal planes and subjected to a horizontal magnetic field, is made. It is found that in the presence of the compressibility effects the magnetic field continues to affect the development of the Rayleigh instability even for disturbances that propagate across the magnetic field (taken perpendicular to gravity), contrary to the result for the case of an incompressible plasma. The special case of a plane interface separating two superposed uniform plasmas of different densities is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the compressibility effects have a stabilising nature.

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Zusammenfassung Es wird die Rayleigh-Instabilität eines kompressiblen Plasmas untersucht, mit Dichte-Schichtung in horizontalen Ebenen, in Gegenwart eines horizontalen Magnetfeldes. Es wird gezeigt, daß bei Kompressibilität das Magnetfeld auch die Instabilitätsentwicklung derjenigen Störungen beeinflußt, die sich quer zum Magnetfeld (welches senkrecht zur Gravitationsrichtung angenommen wurde) fortpflanzen; dies ist im kompressiblen Plasma nicht der Fall. Der Spezialfall einer ebenen Trennfläche zwischen zwei Plasmas mit verschiedenen gleichförmigen Dichten wird behandelt, um den Kompressibilitätseffekt auf die hydromagnetische Rayleigh-Instabilität zu zeigen; dieser erweist sich als stabilisierend.