Hyperbolic partial differential equations and geometric optics. Dec 12, 2012 we consider the classical compressible euler s equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. This paper studies the euler maxwell system which is a model of a collisionless plasma. May 21, 2016 we investigate the compressible navierstokes equations where the constitutive law for the stress tensor given by maxwells law is revised to a system of relaxation equations for two parts of the tensor. The cauchy problem on the compressible twofluids euler maxwell equations renjun duan, qingqing liu, and changjiang zhu abstract. The controlling dimensionless parameter for compressible. We derive incompressible emhd equations from compressible euler maxwell equations via the quasineutral regime. Siam journal on mathematical analysis siam society for. We derive incompressible emhd equations from compressible eulermaxwell equations via the quasineutral regime. Sep, 2007 in this paper, the convergence of timedependent euler maxwell equations to compressible euler poisson equations in a torus via the nonrelativistic limit is studied. The combined nonrelativistic and quasineutral limit of twofluid eulermaxwell equations for plasmas is rigorously justified in this paper. The ninth volume in the outstanding surveys of modern mathematics series from the international press of boston, compressible flow and euler s equations is a 581 page monograph considers the classical compressible euler equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant.
Compressible navierstokes equations with revised maxwells. This system can be reformulated in a form analogous to that of electromagnetism governed by maxwells equations with source terms. Global existence and asymptotic decay of solutions to the. The full set of 1d compressible euler equations permits acoustic waves. For wellprepared initial data, the convergence of the twofluid euler maxwell system to the compressible euler equations is proved in the time interval where a smooth solution of the limit problem. A new formulation of equations of compressible fluids by. There are books 6, 28, 33, 105, 107 and expository articles. The combined quasineutral and nonrelativistic limit of compressible navierstokes maxwell equations for plasmas is studied. A 1d x domain of 3km length with periodic boundary conditions is used to demonstrate the errors inherent in our scheme. The ninth volume in the outstanding surveys of modern mathematics series from the international press of boston, compressible flow and eulers equations is a 581 page monograph considers the classical compressible euler equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant. We consider the classical compressible eulers equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere.
Eulermaxwell system will be more interesting and challenging works. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal. Decay estimates of solutions to the bipolar nonisentropic. Notes on the euler equations stony brook university. In this paper we shall present a numerical algorithm to solve the compressible euler equations in three dimensional geometries with a moving boundary. Jeromey, dehua wang z abstract the euler maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic eld are studied. Incompressible limit of the nonisentropic euler equations with the solid wall boundary conditions alazard, thomas, advances in differential equations, 2005. Under the assumption that the initial data are well prepared for the electric density, electric velocity, and magnetic field but not necessarily for the electric field, the convergence of the solutions of the compressible euler maxwell equations in a torus to the solutions of. Book this book does not require a rating on the projects quality scale. Approximation of a compressible eulerpoisson equations by a. Convergence of compressible eulermaxwell equations to. We investigate the compressible navierstokes equations where the constitutive law for the stress tensor given by maxwells law is revised to a system of relaxation equations for two parts of the tensor. Initial boundary value problem for compressible euler. Convergence of a singular eulermaxwell approximation of.
Abstract pdf 338 kb 2011 relaxation limit and global existence of smooth solutions of compressible eulermaxwell equations. Convergence of the full compressible navierstokesmaxwell. The study of compressible euler maxwell equations began in 2000, chen, jerome and wang 1 prove the existence of global weak solutions of the simplified euler maxwell equations by using the. The eulermaxwell system regarded as a hydrodynamic model for plasma physics describes the dynamics of compressible electrons in a constant, charged, nonmoving ion background. This system has two unknowns u,v, and by the existence of riemann.
Although there have been many results mentioned above that referred to the compressible eulermaxwell system, studies of the full bipolar case are few and far between. Derivation of the compressible euler equations in this section we use the divergence theorem to derive a physical interpretation of the compressible euler equations as the continuum version of newtons laws of motion. Global classical solutions to the compressible eulermaxwell. An adaptive leastsquares method for the compressible euler equations international journal for numerical methods in fluids, vol.
A multiplegrid scheme for solving the euler equations. In this paper, we consider the compressible euler maxwell equations arising in semiconductor physics, which take the form of euler equations for the conservation laws of mass density and current density for electrons, coupled to maxwell s equations for selfconsistent electromagnetic fields. This system can be reformulated in a form analogous to that of electromagnetism governed by maxwell s equations with source terms. Since usually it is required to deal with some complex related problems such as the oscillatory behavior of the electric fields, the. The study of compressible eulermaxwell equations began in 2000, chen, jerome and wang 1 prove the existence of global weak solutions of the simplified eulermaxwell equations by. Mathematical book on maxwell equation mathematics stack. For wellprepared initial data, it is shown that the smooth solution of compressible navierstokesmaxwell equations converges to the smooth solution of incompressible navierstokes equations by introducing new modulated energy functional. Incompressible type euler as scaling limit of compressible. Based on these uniform estimates, we obtain the convergence of the full compressible navierstokes maxwell system to the incompressible magnetohydrodynamic equations for wellprepared data. For well prepared initial data the convergence of solutions. Under the assumption that the initial data are well prepared for the electric density, electric velocity, and magnetic field but not necessarily for the electric field, the convergence of the solutions of the compressible eulermaxwell equations in a torus to the.
Compressible euler equations with damping ronghua pan. Jul 18, 2011 in this paper, we will discuss asymptotic limit of nonisentropic compressible euler maxwell system arising from plasma physics. The global wellposedness is proved as well as the compatibility with the classical compressible navierstokes system in the sense that, for vanishing relaxation parameters, the. Citeseerx document details isaac councill, lee giles, pradeep teregowda. For this new model, we show that for some special large initial data, the life span of. The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. Convergence of compressible eulerpoisson equations to. An introduction to the incompressible euler equations. Furthermore, some recent results about the convergence of nonisentropic compressible euler maxwell system to the compressible euler poisson equations will be given via.
By energy estimation and the curldiv decomposition of the gradient, we rigorously justify a singular approximation of the incompressible euler equations via a quasineutral regime. The rigorous derivations of the emhd equation from vlasovmaxwell system equations by a scaling limit and from eulermaxwell system by a quasineutral regime are obtained, respectively, in and in. Convergence of the eulermaxwell twofluid system to compressible euler equations article in journal of mathematical analysis and applications 4172. Compressible euler equations the compressible euler equations describe the. Scaling limits of nonisentropic eulermaxwell equations. The cauchy problem on the compressible twofluids eulermaxwell equations renjun duan, qingqing liu, and changjiang zhu abstract. Convergence of compressible navierstokesmaxwell equations. In this paper, we consider the compressible eulermaxwell equations arising in semiconductor physics, which take the form of euler equations for the. The combined quasineutral and nonrelativistic limit of compressible navierstokesmaxwell equations for plasmas is studied.
For well prepared initial data the convergence of solutions is rigorously justified by. This book is within the scope of wikiproject physics, a collaborative effort to improve the coverage of physics on wikipedia. Based on these uniform estimates, we obtain the convergence of the full compressible navierstokesmaxwell system to the incompressible magnetohydrodynamic. Removing discretely selfsimilar singularities for the 3d navierstokes equations.
This is a subclass of all euler solutions, but arguably the one most relevant to compressible. Rigorous derivation of incompressible emhd equations from. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. In this paper we establish the uniform estimates of strong solutions with respect to the mach number and the dielectric constant to the full compressible navierstokesmaxwell system in a bounded domain. On the incompressible limit for the compressible flows of liquid crystals under strong stratification on bounded domains kwon, youngsam, abstract and applied analysis, 20. In this paper, we are concerned with the cauchy problem on the compressible isentropic twouids euler maxwell equations in three dimensions. The euler equations can be applied to incompressible and to compressible flow assuming the flow velocity is a solenoidal field, or using another appropriate energy equation respectively the simplest form for euler equations being the conservation of the specific entropy. A controlvolume model of the compressible euler equations. The threedimensional navierstokes equations by james c. Lagrangian coordinate in section 2a, and the equations using the eulerian coordinate in section 2b. Citeseerx solving the compressible euler equations in. The study of compressible eulermaxwell equations began in 2000, chen, jerome and wang 1 prove the existence of global weak solutions of the simplified euler maxwell equations by using the. In this article, the convergence of timedependent and nonisentropic eulermaxwell equations to compressible eulerpoisson equations in a torus via the nonrelativistic limit is studied.
We will solve the euler equations using a highorder godunov methoda. Communications in partial differential equations, vol. In this paper, we study the convergence of timedependent eulermaxwell equations to incompressible type euler equations in a torus via the combined quasineutral and nonrelativistic limit. In this paper, we study the convergence of timedependent euler maxwell equations to incompressible type euler equations in a torus via the combined quasineutral and nonrelativistic limit. The global wellposedness is proved as well as the compatibility with the classical compressible navierstokes system in the sense that, for vanishing relaxation. In addition to the velocity and pressure, the density of the. Formally, we give some different limit systems according to the corresponding different scalings. I think that the best book of such kind is the monograph by claus muller 1969 1, which is the translation of an older 1957 monograph. For wellprepared initial data, the convergence of the twofluid eulermaxwell system to the compressible euler equations is proved in the time interval where a smooth solution of the limit problem. Convergence of the eulermaxwell twofluid system to. The global approximate solutions to the initialboundary value problem are constructed by the fractional godunov scheme. A compressible ideal fluid is governed by euler s equation of motion and equations of continuity, entropy and vorticity.
Many fundamental results are presented for the first time in a textbook format. Compressible eulermaxwell equations guiqiang chen, joseph w. The nonisentropic compressible eulermaxwell system is investigated in. Wang convergence of compressible eulerpoisson equations the purpose of this paper is to study the debye length limit by the method of asymptotic expansion to the cauchy problem for the multidimensional eulerpoisson equations for plasmas with the ion density b being given. This paper studies the eulermaxwell system which is a model of a collisionless plasma. In this paper, we consider the compressible euler maxwell equations arising in semiconductor physics, which take the form of euler equations for the.
Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. The cauchy problem on the compressible twofluids euler. May 01, 2012 studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible euler equations with dense oscillations created by resonant interactions. Global classical solutions to the compressible euler. In fact, the full bipolar eulermaxwell system is more complicated, containing 16 equations. The local existence of smooth solutions to both equations is proved by using energy method for first order symmetrizable hyperbolic systems. They present important open physical and mathematical problems. A global smooth flow with small amplitude is constructed here in three space dimensions when the electron velocity relaxation is taken into account. Compressible navierstokes equations with revised maxwell. The combined nonrelativistic and quasineutral limit of twofluid euler maxwell equations for plasmas is rigorously justified in this paper. In this paper, the convergence of timedependent eulermaxwell equations to compressible eulerpoisson equations in a torus via the nonrelativistic limit is studied. Convergence of a singular eulermaxwell approximation of the. For well prepared initial data, the local existence of smooth solutions to the limit equations is proved by an iterative scheme.
Global existence and asymptotic decay of solutions to the non. In this paper, we are concerned with the cauchy problem on the compressible isentropic twouids eulermaxwell equations in three dimensions. The numerical algorithm consists of a new cellcentered upwind finite volume scheme of higher order on a grid of simplices and the possibility. Historically, only the incompressible equations have been derived by. Moreover, the convergences of solutions of the former to the solutions of. As we shall show, such strong limits are weak solutions of the compressible euler system. For wellprepared initial data, it is shown that the smooth solution of compressible navierstokes maxwell equations converges to the smooth solution of incompressible navierstokes equations by introducing new modulated energy functional. This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. We consider blowup of classical solutions to compressible navierstokes equations with revised maxwells law which can be regarded as a relaxation to the classical newtonian flow. Full compressible navierstokes maxwell system, incompressible magnetohydrodynamic equations, bounded domain. This phenomenon on the charge transport shows the essential relation of the equations with the. Scaling limits of nonisentropic eulermaxwell equations for.
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