# Events for July 24, 2017 from General and Seminar calendars

## Nonlinear Partial Differential Equations

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Bongsuk Kwon, Ulsan National Institute of Science and Technology

**Title:** *Quasi-neutral limit for the Euler-Poisson system*

**Abstract:**We first briefly talk about the formation of a plasma sheath near the surface of a ball-shaped material immersed in a bulk plasma. To mathematically investigate this, we study existence, stability and the quasi-neutral limit of the boundary layer solutions for the Euler-Poisson equations in a three-dimensional annular domain. Under a suitable condition on the velocity at the sheath edge, referred as to Bohm criterion for the annulus, we show that there exists a unique stationary spherical symmetric solution. Then, we show the quasi-neutral limit behavior by establishing $H^1$ estimate of the difference of the solutions to the Euler-Poisson equations and its quasi-neutral limiting equations. If time permits, the stability and asymptotic behavior will be also discussed.