非线性偏微分方程系列报告日程安排
2022年10月21日上午
（腾讯会议：ID 631990282）
时间 
开幕式主持人：蒲学科 
08:4509:00 
彭济根院长致辞、郭柏灵院士致辞 

主持人 
报告人 
题目 
09:0009:30 
丁时进 
霍朝辉 
Wellposedness for the initial boundary problem of the generalized derivative nonlinear Schr\"odinger equation on the halfline for any large initial data 
09:3010:00 
李用声 
黄代文 
On the attractors of primitive equations of the largescale atmosphere and ocean 
10:0010:30 
房少梅 
张景军 
Global solution for equations governing thelowfrequency ion motion in plasma 
10:3010:40 
茶歇 

主持人 
报告人 
题目 
10:4011:10 
韩永前 
江杰 
The Effect of Signaldependent Motility in a KellerSegel System of Chemotaxis 
11:1011:40 
唐春雷 
李景 
Finite volume method for distributedorder diffusionadvection equations 
11:4014:00 

午餐 
2022年10月21日下午

主持人 
报告人 
题目 
14:0014:30 
王保祥 
凌黎明 
The robust inverse scattering method for focusing Ablowitz–Ladik equation on the nonvanishing background 
14:3015:00 
高洪俊 
吴兴龙 
Some new results of the dD Euler equations 
15:0015:30 
刘正荣 
边东芬 
On the BoussinesqMHD system. 
15:3015:40 

茶歇 

主持人 
报告人 
题目 
15:4016:10 
孟凡伟 
郭春晓 
A Nonhomogeneous Initial BoundaryValue Problem for the Hirota Equation Posed on the Half Line. 
16:1016:40 
辛杰 
高金城 
Optimal decay of compressible NavierStokes equations with or without potential force 
组织者：
蒲学科，15876515526
王光武，18810995968
报告摘要
Wellposedness for the initial boundary problem of the generalized derivative nonlinear Schr\"odinger equation on the halfline for any large initial data
霍朝辉副研究员（中国科学院数学与系统科学研究院）
摘要：We cansider the wellposedness of the initial boundary for the generalized derivative nonlinear Schr\"odinger equation on the halfline
$$u_{t}iu_{xx}=F( u,\bar{u}, u_x,\bar{u}_x), \ \ x\geq0;$$
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 wellposed 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 wellposed in $ C([T,T]:H_x^{s}) $ with $s>3/2$ for any large initial data.
On the attractors of primitive equations of the largescale atmosphere and ocean
黄代文研究员（北京应用物理与计算数学研究所）
摘要：In this talk, we give some results on the attractors of primitive equations
of the largescale ocean. Firstly, we recall the global
wellposedness and longtime dynamics for the viscous primitive
equations describing the largescale 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 lowfrequency ion motion in plasma
张景军教授（嘉兴学院）
摘要：We consider the equations describing the interactions between Langmuir waves and the lowfrequency response of ions. Using the analysis of higher order energy estimate and lower order decay estimate, existence of global smooth solution is established for suitably small initial data.
The Effect of Signaldependent Motility in a KellerSegel System of Chemotaxis
江杰副研究员（中国科学院精密测量科学与技术创新研究院）
摘要：In this talk, we would like to report our recent work on a Keller—Segel system of chemotaxis involving signaldependent motility. This model was originally proposed by Keller and Segel in their seminal work in 1971, and has been used to provide a new mechanism for pattern formation in some recent Biophysics work published in Science and PRL.
From a mathematical point of view, the model features a nonincreasing signaldependent motility function, which may vanish as the concentration becomes unbounded, leading to a possible degenerate problem. We develop systematic new methods to study the wellposedness 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 infinitetime blowup was verified in the twodimensional 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 distributedorder diffusionadvection equations
李景副教授（长沙理工大学）
摘要：In this talk, we investigate the finite volume method (FVM) for a distributedorder spacefractional advection–diffusion (AD) equation. The midpoint quadrature rule is used to approximate the distributedorder equation by a multiterm fractional model. Next, the transformed multiterm fractional equation is solved by discretizing in space by the finite volume method and in time using the Crank–Nicolson scheme. We use a novel technique to deal with the convection term, by which the Riesz fractional derivative of order 0 < γ < 1 is transformed into a fractional integral form. An important contribution of our work is the use of nodal basis function to derive the discrete form of our model. The unique solvability of the scheme is also discussed and we prove that the Crank–Nicolson scheme is unconditionally stable and convergent with secondorder accuracy.
The robust inverse scattering method for focusing Ablowitz–Ladik equation on the nonvanishing background
凌黎明教授（华南理工大学）
报告摘要： In this talk, we consider the robust inverse scattering method for the Ablowitz–Ladik (AL) equation on the nonvanishing background, which can be used to deal with arbitraryorder poles on the branch points and spectral singularities in a unified way. The Darboux matrix is constructed with the aid of loop group method and considered within the framework of robust inverse scattering transform. Various soliton solutions are constructed without using the limit technique. These solutions include general soliton, breathers, as well as high order rogue wave solutions. (joint with Y. Chen and B.F. Feng)
Some new results of the dD Euler equations
吴兴龙教授（武汉理工大学）
摘要：In this talk, we will recall some new progress in theory for the dD Euler equations (such as global existence and blowup), and present the relation between regularity of solution and energy conservation for the inhomogeneous incompressible and compressible Euler equations.
On the BoussinesqMHD system
边东芬副教授（北京理工大学）
报告摘要: In this talk, we will show the stability for the BoussinesqMHD system with partial dissipation. This is based on joint works with Xintong Ji, Jingjing Mao and Xueke Pu.
A Nonhomogeneous Initial BoundaryValue Problem for the Hirota Equation Posed on the Half Line.
郭春晓教授（中国矿业大学（北京））
报告摘要: We study a system described by a class of initial and boundary value problem (IBVP) of the Hirota equation posed on a half line with nonhomogeneous boundary conditions. In particular, using an explicit solution formula and contraction mapping ethod, we prove the local wellposedness of the IBVP in the Sobolev space $H^s (R^+)$ for any $s\geq 0$, and then we obtain the global wellposedness by the energy estimates of solution. The main difficulties of this model are caused by that the characteristic equation corresponding to Hirota equation is complicated and needs to be solved by construction, beyond that the Kato smoothness of the nonlinear terms $i\gamma(u^2u)_x$ and $u^2u$ are taken into consideration.
Optimal decay of compressible NavierStokes equations with
or without potential force
高金城副教授（中山大学）
摘要：In this talk, we investigate the optimal decay rate for the higher orderspatial derivative of globalsolution to the compressible NavierStokes equations with or without potential force in threedimensional whole space. We will show that the higher order derivative of global solution will decay faster than the lower one.