10:00-10:50   Shiwu Yang (Peking University)

Title: A scattering theory for the Maxwell-Klein-Gordon equations

Abstract: It has been shown that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space decay like linear solutions. One hence can define the associated radiation field on the future null infinity. In this talk, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem to the MKG system with general large data by using gauge invariant vector field method. This is based on joint work with W. Dai, H. Mei and D. Wei.

11:10-12:00  Yusuke Ishigaki (Osaka University)

Title: Asymptotic stability of stationary solutions to outflow problem for compressible viscoelastic system in one dimensional half space

Abstract: We investigate the existence and stability of stationary solutions to the outflow problem for compressible viscoelastic system in the one-dimensional half space. We classify the existence of stationary solutions by determining suitable conditions for several parameters, such as the Mach number and propagation speed of elastic wave. We next establish its stability result under the small initial perturbation. This talk is based on a joint work with Yoshihiro Ueda (Kobe University).

13:30-14:20  Baoping Liu (Peking University)

Title: Wellposedness and scattering for defocusing energy subcritical nonlinear wave equation

Abstract:   We consider the power type defocusing energy subcritical nonlinear wave equation with inverse square potential in dimensions 3, 4, 5. By exploring the idea of Dodson, we prove that solution exists globally and scatters for radial data lying in critical space.

14:40-15:30  Masanari Miura (Yamato University)

Title: On pointwise space-time decay of solutions to the Keller-Segel system of parabolic-elliptic type

Abstract: The Keller-Segel system, classified as an advection-diffusion equation, has multiple parameters, and their choice leads to a rich variety of structures, including parabolic-parabolic, parabolic-elliptic, as well as semilinear, degenerate, and singular types. It is well known that global-in-time solutions exist for small initial data, and that the spatial $L^p$ norm of solutions decays with time. However, the decay properties at each point in space-time have been open problems. In this talk, we focus on the semilinear Keller-Segel system of parabolic-elliptic type in general spatial dimensions and demonstrate the existence of solutions with optimal pointwise space-time decay rates in a certain weighted $L^\infty$ space. This is a joint work with Kosuke Shibata (Osaka University) and Yoshie Sugiyama (Osaka University).

15:50-16:40  Chenjie Fan (Chinese Academy of Sciences)

Title: Scattering for SNLS with a small noise

Abstract: Abstract：We present our proof of scattering for mass critical NLS with a small multiplicative noise. As a byproduct or as a toy model of our analysis, we also obtain the associated global in time Strichartz type estimates for the related linear model. Though some stochastic background is necesary in the proof, this is essentially a determinitic PDE talk. Based on joint work with Weijun Xu and Zehua Zhao.

17:00-17:50  Takayoshi Ogawa (Tohoku University) 

TBA