主讲人：朱长江 教授（华中师范大学）

时  间：2014年4月25日（周五）15:00-16:00

地  点：必赢76net线路官网北二区教学楼 510 教室

摘  要：This talk is concerned with the large time behavior of Euler-Maxwell system. I will present three results. Our first attempt on two-fluid Euler-Maxwell system is a Cauchy problem on a simplified version where we set all physical parameters to be 1. In this case, the linearized equations around constant equilibrium can be decomposed into one-fluid Euler-Maxwell equations and damped Euler equations. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and the time-decay rates of perturbed solutions in $L^q$ space for $2\leq q \leq \infty$ are obtained. When the ions are non-moving and become a uniform non-trivial background density $n_{b}(x)$, a one-fluid Euler-Maxwell model is formally derived. In this case, the naturally existing steady states of system are no longer constants $[1, 0, 0, 0]$, we consider the asymptotic stability of stationary solutions. Recently, we studied the original Euler-Maxwell system with all physical parameters. It turns out that both the density and the magnetic field tend time-asymptotically to the diffusion equations with diffusive coefficients explicitly determined by given physical parameters with the rate $(1+t)^{-5/4} in L^{2}$ norm. And the velocities and the electric field tend time-asymptotically to the corresponding asymptotic profiles given in the sense of the generalized Darcy's law with the faster rate $(1 + t)^{-7/4}$ in $L^2$ norm. These are some joint works with Renjun Duan and Qingqing Liu.