PDE seminar: Existence of the stationary solutions and its asymptotic stability for non-isentropic Euler-Maxwell system

2013-12-2 16:30 - 2013-12-2 17:30
Faculty of Science Building #3, Room 309
Yoshihiro Ueda (Kobe University)
In this talk, we consider the Cauchy problem of the nonisentropic
Euler-Maxwell system. The Euler-Maxwell system
describes the dynamics of compressible electrons in plasma
physics under the interaction of the magnetic and electric
fields via the Lorentz force. Our purpose is to study the
large-time behavior of solutions to the initial value problem
for the non-isentropic Euler-Maxwell system. This system
verifies the dissipative property of the regularity-loss type.
We first consider the stationary problem and derive the existence
of the stationary solution. Moreover, under smallness
condition on the initial perturbation and the amplitude of
stationary solution, we show that the solution to the problem
exists globally in time and converges to the stationary solution.
This talk is based on a joint work with Shuichi Kawashima
(Kyushu University).