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# 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.