20221021日上午

（腾讯会议：ID 631-990-282­­­

 时间 开幕式主持人：蒲学科 08:45-09:00 彭济根院长致辞、郭柏灵院士致辞 主持人 报告人 题目 09:00-09:30 丁时进 霍朝辉 Well-posedness for the initial boundary problem of the generalized derivative nonlinear Schr\"odinger equation on the half-line for any large initial data 09:30-10:00 李用声 黄代文 On the attractors of primitive equations of the large-scale atmosphere and ocean 10:00-10:30 房少梅 张景军 Global solution for equations governing thelow-frequency ion motion in plasma 10:30-10:40 茶歇 主持人 报告人 题目 10:40-11:10 韩永前 江杰 The Effect of Signal-dependent Motility in a Keller--Segel System of Chemotaxis 11:10-11:40 唐春雷 李景 Finite volume method for distributed-order diffusion-advection equations 11:40-14:00 午餐

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20221021日下午

 主持人 报告人 题目 14:00-14:30 王保祥 凌黎明 The robust inverse scattering method for focusing Ablowitz–Ladik equation on the non-vanishing background 14:30-15:00 高洪俊 吴兴龙 Some new results of the d-D Euler equations 15:00-15:30 刘正荣 边东芬 On the Boussinesq-MHD system. 15:30-15:40 茶歇 主持人 报告人 题目 15:40-16:10 孟凡伟 郭春晓 A Nonhomogeneous Initial Boundary-Value Problem for the Hirota Equation Posed on the Half Line. 16:10-16:40 辛杰 高金城 Optimal decay of compressible Navier-Stokes equations with or without potential force

Well-posedness for the initial boundary problem of the generalized derivative nonlinear Schr\"odinger equation on the half-line for any large initial data

$$u_{t}-iu_{xx}=F( u,\bar{u}, u_x,\bar{u}_x), \ \ x\geq0;$$

where $F : \C^{4} \rightarrow \C$ is a polynomial with no constant or linear terms and no quadratic terms. We can show that the initial boundary problem is locally well-posed in $C([-T,T]:H_x^{s})\bigcap C_x((0,\infty): H_t^{(2s+1)/4})$ with $s>3/2$ for any large initial data.

Moreover, using the above method, we can show that the Cauchy problem of the derivative nonlinear Schr\"odinger equation on the real line

$$u_{t}-iu_{xx}=F( u,\bar{u}, u_x,\bar{u}_x), \ \ (x,t) \in \R \times \R;$$

is locally well-posed in $C([-T,T]:H_x^{s})$ with $s>3/2$ for any large initial data.

On the attractors of primitive equations of the large-scale atmosphere and ocean

of the large-scale ocean. Firstly, we recall the global

well-posedness and long-time dynamics for the viscous primitive

equations describing the large-scale oceanic motion . Secondly, we introduce some results on the global attractros of

primitive equations, such as the enhanced pullback attractors of 3D Primitive Equations.

Global solution for equations governing the low-frequency ion motion in plasma

The Effect of Signal-dependent Motility in a Keller--Segel System of Chemotaxis

From a mathematical point of view, the model features a non-increasing signal-dependent motility function, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. We develop systematic new methods to study the well-posedness problem. The key idea lies in an introduction of an elliptic auxiliary problem which enables us to apply delicate comparison arguments to derive the upper bound of concentration. Moreover, new iteration as well as monotonicity techniques are developed to study the global existence of classical solutions and their boundedness in any dimension. It is shown that the dynamic of solutions is closely related to the decay rate of the motility function at infinity. In particular, a critical mass phenomenon as well as an infinite-time blowup was verified in the two-dimensional case if the motility is a negative exponential function.

The talk is based on my recent joint works with Kentarou Fujie (Tohoku University), Philippe Laurençot (University of Toulouse and CNRS), Yanyan Zhang (ECNU), and Yamin Xiao (IAPCM).

Finite volume method for distributed-order diffusion-advection equations

The robust inverse scattering method for focusing Ablowitz–Ladik equation on the non-vanishing background

Some new results of the d-D Euler equations

On the Boussinesq-MHD system

A Nonhomogeneous Initial Boundary-Value Problem for the Hirota Equation Posed on the Half Line.

Optimal decay of compressible Navier-Stokes equations with

or without potential force