Stability of the neutral state for the 2 fluid Euler-Maxwell system

Stability of the neutral state for the 2 fluid Euler-Maxwell system

-
Benoit Pausader, Princeton University
Fine Hall 314

This is a joint work with Y. Guo and A. Ionescu. We consider the 2 fluid Euler-Maxwell problem in the whole 3d space. We show that small and smooth irrotational initial perturbations lead to solutions which remain globally smooth and scatter back to equilibrium. This shows a stabilization effect due to the electromagnetic field since in the absence of electromagnetic field, a classical result of Sideris shows that formation of shock is expected for compressible fluids.   The proof consists of a combination of energy estimates to provide a first rough control and nonlinear stationary phase estimates to obtain decay of the solution. However the presence of electron accoustic wave introduces new degeneracies in the phase functions.