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. Communications in partial differential equations, vol. Citeseerx document details isaac councill, lee giles, pradeep teregowda. 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. This paper studies the euler maxwell system which is a model of a collisionless plasma. 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. The cauchy problem on the compressible twofluids eulermaxwell equations renjun duan, qingqing liu, and changjiang zhu abstract.
We derive incompressible emhd equations from compressible eulermaxwell equations via the 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. Initial boundary value problem for compressible euler. Based on these uniform estimates, we obtain the convergence of the full compressible navierstokesmaxwell system to the incompressible magnetohydrodynamic. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength. Moreover, the convergences of solutions of the former to the. Removing discretely selfsimilar singularities for the 3d navierstokes equations. The nonisentropic compressible eulermaxwell system is investigated in. Siam journal on mathematical analysis siam society for. 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.
A 1d x domain of 3km length with periodic boundary conditions is used to demonstrate the errors inherent in our scheme. Rigorous derivation of incompressible emhd equations from. An adaptive leastsquares method for the compressible euler equations international journal for numerical methods in fluids, vol. Convergence of the eulermaxwell twofluid system to compressible euler equations article in journal of mathematical analysis and applications 4172. 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. 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. In this paper, we consider the compressible euler maxwell equations arising in semiconductor physics, which take the form of euler equations for the. 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. The numerical algorithm consists of a new cellcentered upwind finite volume scheme of higher order on a grid of simplices and the possibility. Convergence of compressible eulerpoisson equations to. 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. 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. Then one gets the nonisentropic incompressible euler equations 1.
Convergence of compressible navierstokesmaxwell equations. A compressible ideal fluid is governed by eulers equation of motion and equations of continuity, entropy and vorticity. Since usually it is required to deal with some complex related problems such as the oscillatory behavior of the electric fields, the. The combined quasineutral and nonrelativistic limit of compressible navierstokes maxwell equations for plasmas is studied.
Formally, we give some different limit systems according to the corresponding different scalings. Compressible flow find the jacobian and the right eigenvectors for eulers equations in 1d, hint. The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. Global classical solutions to the compressible eulermaxwell. Moreover, the convergences of solutions of the former to the solutions of. In this paper, we consider the compressible eulermaxwell equations arising in semiconductor physics, which take the form of euler equations for the. Global existence and asymptotic decay of solutions to the. The cauchy problem on the compressible twofluids euler maxwell equations renjun duan, qingqing liu, and changjiang zhu abstract. 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. Since usually it is required to deal with some complex related problems such as the oscillatory behavior of the electric fields. 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. This system can be reformulated in a form analogous to that of electromagnetism governed by maxwell s equations with source terms. 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. Scaling limits of nonisentropic eulermaxwell equations for.
They present important open physical and mathematical problems. Historically, only the incompressible equations have been derived by. Mathematical book on maxwell equation mathematics stack. 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. An introduction to the incompressible euler equations. A controlvolume model of the compressible euler equations. Decay estimates of solutions to the bipolar nonisentropic.
In 7, the incompressible euler equation 2 of ideal fluid from the emhd system 1 via a nonrelativistic limit was gotten only in formal. Full compressible navierstokes maxwell system, incompressible magnetohydrodynamic equations, bounded domain. In this paper, we are concerned with the cauchy problem on the compressible isentropic twouids euler maxwell equations in three dimensions. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. The combined nonrelativistic and quasineutral limit of twofluid eulermaxwell 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. In this paper we shall present a numerical algorithm to solve the compressible euler equations in three dimensional geometries with a moving boundary. 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. Compressible eulermaxwell equations guiqiang chen, joseph w.
Jul 18, 2011 in this paper, we will discuss asymptotic limit of nonisentropic compressible euler maxwell system arising from plasma physics. A new formulation of equations of compressible fluids by. The local existence of smooth solutions to both equations is proved by using energy method for first order symmetrizable hyperbolic systems. Abstract pdf 338 kb 2011 relaxation limit and global existence of smooth solutions of compressible eulermaxwell equations. For well prepared initial data, the local existence of smooth solutions to the limit equations is proved by an iterative scheme. In fact, the full bipolar eulermaxwell system is more complicated, containing 16 equations. This phenomenon on the charge transport shows the essential relation of the equations with the. This system has two unknowns u,v, and by the existence of riemann. Book this book does not require a rating on the projects quality scale. 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. A multiplegrid scheme for solving the euler equations.
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. Jeromey, dehua wang z abstract the euler maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic eld are studied. It is shown that the density and temperature of electron converge to the equilibrium states at the same rate in l q norm. Eulermaxwell system will be more interesting and challenging works. Citeseerx solving the compressible euler equations in. This paper studies the eulermaxwell system which is a model of a collisionless plasma. Incompressible type euler as scaling limit of compressible. Furthermore, some recent results about the convergence of nonisentropic compressible euler maxwell system to the compressible euler poisson equations will be given via. 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. Notes on the euler equations stony brook university. 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.
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. A compressible ideal fluid is governed by euler s equation of motion and equations of continuity, entropy and vorticity. Compressible navierstokes equations with revised maxwell. Global classical solutions to the compressible euler. Lagrangian coordinate in section 2a, and the equations using the eulerian coordinate in section 2b. Convergence of the full compressible navierstokesmaxwell. The combined nonrelativistic and quasineutral limit of twofluid euler maxwell equations for plasmas is rigorously justified in this paper. In this article, the convergence of timedependent and nonisentropic eulermaxwell equations to compressible eulerpoisson equations in a torus via the nonrelativistic limit is studied. The threedimensional navierstokes equations by james c. Convergence of a singular eulermaxwell approximation of the.
Based on these uniform estimates, we obtain the convergence of the full compressible navierstokes maxwell system to the incompressible magnetohydrodynamic equations for wellprepared data. 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. The combined quasineutral and nonrelativistic limit of compressible navierstokesmaxwell equations for plasmas is studied. There are books 6, 28, 33, 105, 107 and expository articles. 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. 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. The controlling dimensionless parameter for compressible. 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. 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. This system can be reformulated in a form analogous to that of electromagnetism governed by maxwells equations with source terms.
Incompressible limit of the nonisentropic euler equations with the solid wall boundary conditions alazard, thomas, advances in differential equations, 2005 on the incompressible limit for the compressible flows of liquid crystals under strong stratification on bounded domains kwon, youngsam, abstract and applied analysis, 20. 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. Hyperbolic partial differential equations and geometric optics. For well prepared initial data the convergence of solutions.
Compressible navierstokes equations with revised maxwells. We will solve the euler equations using a highorder godunov methoda. In this paper, we are concerned with the cauchy problem on the compressible isentropic twouids eulermaxwell equations in three dimensions. In addition to the velocity and pressure, the density of the. 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. For well prepared initial data the convergence of solutions is rigorously justified by.
The full set of 1d compressible euler equations permits acoustic waves. Scaling limits of nonisentropic eulermaxwell equations. 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. 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. Compressible euler equations the compressible euler equations describe the. Compressible euler equations with damping ronghua pan. Convergence of the eulermaxwell twofluid system to.
The eulermaxwell system regarded as a hydrodynamic model for plasma physics describes the dynamics of compressible electrons in a constant, charged, nonmoving ion background. Approximation of a compressible eulerpoisson equations by a. 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. A global smooth flow with small amplitude is constructed here in three space dimensions when the electron velocity relaxation is taken into account. 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. 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. We derive incompressible emhd equations from compressible euler maxwell equations via the quasineutral regime. On the incompressible limit for the compressible flows of liquid crystals under strong stratification on bounded domains kwon, youngsam, abstract and applied analysis, 20. This book is within the scope of wikiproject physics, a collaborative effort to improve the coverage of physics on wikipedia. 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. Global existence and asymptotic decay of solutions to the non.
The cauchy problem on the compressible twofluids euler. For this new model, we show that for some special large initial data, the life span of. Approximation of a compressible eulerpoisson equations by. Convergence of compressible eulermaxwell equations to. The global approximate solutions to the initialboundary value problem are constructed by the fractional godunov scheme. This is a subclass of all euler solutions, but arguably the one most relevant to compressible. Incompressible limit of the nonisentropic euler equations with the solid wall boundary conditions alazard, thomas, advances in differential equations, 2005. The global wellposedness is proved as well as the compatibility with the classical compressible navierstokes system in the sense that, for vanishing relaxation. As we shall show, such strong limits are weak solutions of the compressible euler system. Many fundamental results are presented for the first time in a textbook format.