Non-isentropic Euler-Maxwell System Research Articles

Zero-Relaxation Limits of the Non-Isentropic Euler–Maxwell System for Well/Ill-Prepared Initial Data

Zero-Relaxation Limits of the Non-Isentropic Euler–Maxwell System for Well/Ill-Prepared Initial Data

Uniform global convergence of non-isentropic Euler–Maxwell systems with dissipation

The purpose of this paper is to investigate uniformly global smooth solutions to the Cauchy problem for a non-isentropic Euler–Maxwell system with velocity dissipation and small physical parameters. As the parameters go to zero, we prove that the quasi-neutral limit of the non-isentropic Euler–Maxwell system is the e-MHD system and the linear transport equation for temperature, while its non-relativistic quasi-neutral limit is the incompressible Euler equation and the linear transport equation for temperature. The uniform energy estimates are achieved through controlling the divergence and the curl of the velocity, the electric and magnetic fields.

Stability of periodic steady-state solutions to a non-isentropic Euler–Maxwell system

This paper is concerned with a stability problem in a periodic domain for a non-isentropic Euler–Maxwell system without temperature diffusion term. This system is used to describe the dynamics of electrons in magnetized plasmas when the ion density is a given smooth function which can be large. When the initial data are close to the steady states of the system, we show the global existence of smooth solutions which converge toward the steady states as the time tends to infinity. We make a change of unknown variables and choose a non-diagonal symmetrizer of the full Euler equations to get the dissipation estimates. We also adopt an induction argument on the order of derivatives of solutions in energy estimates to get the stability result.

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.

Global existence and decay of solution for the nonisentropic Euler–Maxwell system with a nonconstant background density

In this paper, the Cauchy problem for the nonisentropic Euler–Maxwell system with a nonconstant background density is studied. The global existence of classical solution is constructed in three space dimensions provided the initial perturbation is sufficiently small. The proof is mainly based on classical energy estimate and the techniques of symmetrizer. And the time decay of the solution is also established by combining the decay estimate of the Green’s function with some time-weighted estimate.

Global existence and asymptotic decay of solutions to the non-isentropic Euler–Maxwell system

The non-isentropic compressible Euler–Maxwell system is investigated in ℝ3 in this paper, and the Lq time decay rate for the global smooth solution is established. It is shown that the density and temperature of electron converge to the equilibrium states at the same rate [Formula: see text] in Lq norm. This phenomenon on the charge transport shows the essential relation of the equations with the non-isentropic Euler–Maxwell and the isentropic Euler–Maxwell equations.

Large-time behavior of solutions to the compressible non-isentropic Euler–Maxwell system in [formula omitted

We first refine the global existence of solutions by assuming that the initial data is small in the H3 norm but the higher order derivatives could be large. If further the initial data belongs to Ḣ−s (0≤s<3/2) or Ḃ2,∞−s (0<s≤3/2), we obtain the various decay rates of the solution and its higher order derivatives. In particular, the decay rates of the density and temperature of electron could reach to (1+t)−134 in L2 norm.