Green's function and Large time behavior for the 1-D compressible Euler-Maxwell system

2025/04/29 by Liang, Boyu, Zhong, Mingying
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.20382

Abstract

We study Green's function and the large time behavior of the one-dimensional Euler-Maxwell System with relaxation. Firstly, we construct the Green's function of linearized system and obtain the optimal time decay rates of its solutions. And then, we obtain the global existence and the optimal time decay rates of solutions to the nonlinear system by using Green's function and a suitable energy estimate.

Citations

• A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system
• Convergence rates in zero-relaxation limits for Euler-Maxwell and Euler-Poisson systems
• Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations
• Asymptotic stability of stationary solutions to the compressible Euler-Maxwell equations
• Global Smooth Flows for the Compressible Euler-Maxwell System: Relaxation Case
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Stability of non-constant equilibrium solutions for Euler–Maxwell equations
• Asymptotic stability of the compressible Euler-Maxwell equations to Euler-Poisson equations

Related

• Green's function and large time behavior of the Navier-Stokes-Maxwell system
• A new characterization of the dissipation structure and the relaxation limit for the compressible Euler-Maxwell system
• Global existence and asymptotic decay of solutions to the Non-isentropic Euler-Maxwell system
• Global solutions of Euler-Maxwell equations with dissipation
• Global convergence rates in the relaxation limits for the compressible Euler and Euler-Maxwell systems in Sobolev spaces