### Absence of shocks in Euler-Maxwell system for two-fluid models in plasma

- Series
- School of Mathematics Colloquium
- Time
- Thursday, April 23, 2015 - 11:01 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Yan Guo – Brown University

As the cornerstone of two-fluid models in plasma theory,
Euler-Maxwell (Euler-Poisson) system describes the dynamics of compressible
ion and electron fluids interacting with their own self-consistent electromagnetic field. It is
also the origin of many famous dispersive PDE such as KdV, NLS, Zakharov,
...etc. The electromagnetic interaction produces plasma frequencies which enhance
the dispersive effect, so that smooth initial data with small amplitude
will persist forever for the Euler-Maxwell system, suppressing any possible shock
formation. This is in stark contrast to the classical Euler system for a
compressible neutral fluid, for which shock waves will develop
even for small smooth initial data. A survey along this direction for
various two-fluid models will be given during this talk.