Georgia Institute of Technology College of Sciences

The Euler-Maxwell system describes the interaction between a compressible fluid of electrons over a background of fixed ions and the self-consistent electromagnetic field created by the motion.We show that small irrotational perturbations of a constant equilibrium lead to solutions which remain globally smooth and return to equilibrium. This is in sharp contrast with the case of neutral fluids where shock creation happens even for very nice initial data.Mathematically, this is a quasilinear dispersive system and we show a small data-global solution result. The main challenge comes from the low dimension which leads to slow decay and from the fact that the nonlinearity has some badly resonant interactions which force a correction to the linear decay. This is joint work with Yu Deng and Alex Ionescu.