13:00 - 14:00

Bongsuk Kwon (Ulsan National Institute of Science and Technology)

**Small Debye length limit for the Euler-Poisson system**

14:20 - 15:20

Chun-Hsiung Hsia(National Taiwan University)

**On the mathematical analysis of synchronizations**

15:50 - 16:50

Ryo Takada (Kyushu University)

**Strongly stratified limit for the 3D inviscid Boussinesq equations**

Abstract 1 (Bongsuk Kwon (Ulsan National Institute of Science and Technology)):

We discuss existence, time-asymptotic behavior, and quasi-neutral limit for the Euler-Poisson equations. Specifically we construct the global-in-time solution of the plasma sheath in the regime of Bohm's criterion, and investigate the properties of the solution including the time-asymptotic behavior and small Debye length limit. If time permits, some key features of the proof and related problems will be discussed. This is joint work with C.-Y. Jung (UNIST) and M. Suzuki (Nagoya Inst. Tech.).

Abstract 2 (Chun-Hsiung Hsia(National Taiwan University)):

The phenomena of synchronization can be easily found in a variety of natural systems. The first reported observation of synchronization is one Dutch scientist’s discovery: Christiaan Huygens realized that two pendulum clocks hanging on the wall have always ended up swinging in exactly the opposite direction from each other in 1665. Since then, people have recognized synchronization phenomena in various areas including circadian rhythms, electrical generators, Josephson junction arrays, intestinal muscles, menstrual cycles, and fire flies. Although it is studied in many different scientific disciplines such as applied mathematics, biology and nonlinear dynamics, the underlying mechanism of synchronization has remained a mystery. Among a number of mathematical models, the differential equations proposed by Kuramoto and Winfree have received considerable attention. In this lecture, we shall present a mathematical analysis for the Kuramoto model. In particular, we shall focus on the time-delayed effect.

Abstract 3 (Ryo Takada (Kyushu University)):

In this talk, we consider the initial value problem of the 3D inviscid Boussinesq equations for stably stratified fluids. We prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the long time classical solution converges to that of 2D incompressible Euler equations in some space-time Strichartz norms.