Global well-posedness for 3D Euler-Maxwell two-fluids system

In this paper, we are concerned with the initial boundary value problem on the partially damped "two fluid" Euler-Maxwell equations in three dimensional periodic domain. Com-pared with the previous "two fluid" Euler-Maxwell results, our model describes two fluids obey different dynamical evolutions, one is compressible Euler and the other is compressible Euler with damping. The global existence of small smooth solutions near constant steady states is established and the time decay rates of perturbed solutions are obtained. The main challenge is to investigate the asymmetric system and find out the transmission mechanism of dissipation. Although there are various variables obeying different dynamical evolutions, we can still derive the unified time-weighted energy frame to achieve our goal. Our theorem in this paper shows that partially damped "two fluid" Euler-Maxwell system (namely mu(+)>0,mu-=0) also yields the global stability of a constant background.