学术报告第一分会场
报告时间：2022年9月11日，8：00-11：50，14：00-18：10
报告地点：腾讯会议：447-613-808
报告题目1：薛定谔流的诺依曼边值问题
报告人1：王友德教授(中国科学院数学与系统科学研究院&广州大学)
报告时间：8：20-9：00
报告题目2：Global Cauchy problems for the nonlocal (derivative) NLS
报告人2：王保祥教授(集美大学)
报告时间：9：00-9：40
报告题目3：稳态磁流体方程组的边界层展开问题
报告人3：丁时进教授(华南师范大学)
报告时间：9：40-10：20
报告题目4：Coexistence of chemostat model with diffusion
报告人4：吴建华教授(陕西师范大学)
报告时间：10：30-11：10
报告题目5：Abundant explicit non-travelling wave solutions for the (2+1)- dimensional breaking soliton equation
报告人5：尚亚东教授(广州大学)
报告时间：11：10-11：50
报告题目6：Global well-posedness of one new class of initial-boundary value problem on incompressible Navier-Stokes equations and the related models
报告人6：王术教授(广州大学&北京工业大学)
报告时间：14：00-14：40
报告题目7：Dyadic modified inhomogeneous and homogeneous energies method
and application for the dispersive limit of the one dimensional fourth
order Schrödinger equation
报告人7：霍朝辉研究员(中国科学院数学与系统科学研究院)
报告时间：14：40-15：20
报告题目8：On the attractors of primitive equations of the large-scale atmosphere and ocean
报告人8：黄代文研究员(北京应用物理与计算数学研究所)
报告时间：15：20-16：00
报告题目9：Asymptotic limit of the Navier-Stokes-Poisson-Korteweg system in the half-space
报告人9：蒲学科教授(广州大学)
报告时间：16：10-16：50
报告题目10：Global solution for equations governing the low-frequency ion motion in plasma
报告人10：张景军教授(嘉兴学院)
报告时间：16：50-17：30
报告题目11：A Nonhomogeneous Initial Boundary-Value Problem for the Hirota
Equation Posed on the Half Line
报告人11：郭春晓教授(中国矿业大学(北京))
报告时间：17：30-18：10
第二分会场
报告时间：2022年9月11日，10：30-11：50，14：00-17：30
报告地点：腾讯会议：270-866-603
报告题目1：The Existence of Three-Dimensional Multi-Hump Gravity-Capillary Surface Waves on Water of Finite Depth
报告人1：邓圣福教授(华侨大学)
报告时间：10：30-11：10
报告题目2：Dispersive blow-up for the KdV equation in Sobolev space
报告人2：韩励佳教授(华北电力大学)
报告时间：11：10-11：50
报告题目3：Some new kink type solutions for the new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation
报告人3：郭艳凤教授(中国地质大学(武汉))
报告时间：14：00-14：40
报告题目4：Existence and asymptotic behaviour of solutions for classes of Schrödinger-Poisson systems
报告人4：丁凌教授(湖北文理学院)
报告时间：14：40-15：20
报告题目5：分布阶对流扩散方程的有限体积法
报告人5：李景教授(长沙理工大学)
报告时间：15：20-16：00
报告题目6：Global well-posedness of 3D Burgers equation with a multiplicative noise force
报告人6：周国立教授(重庆大学)
报告时间：16：10-16：50
报告题目7：Onset of nonliear instabilities in monotonic viscous boundary layers
报告人7：边东芬教授(北京理工大学)
报告时间：16：50-17：30
邀请人：刘正荣教授、李用声教授、凌黎明教授
欢迎广大师生参加！
数学学院 2022年9月6日
第一分会场报告摘要
报告1摘要：我们将回顾作为薛定谔流的物理背景的Landau-Lifshitz方程及其相关方程的历史, 及其此方程与物理学（微电子学）、材料科学、流体力学的紧密联系. 另一方面, 也回顾此类方程与微分几何与拓扑学之间自然的联系. 最后, 介绍我们最近就薛定谔流（Landau-Lifshitz方程）的初始-诺依曼边值问题的强解及光滑解的存在性所取得的进展.
报告2摘要：We consider the Cauchy problem for the (derivative) nonlocal NLS in super-critical function spaces E^{s}_{σ}. Any Sobolev space H^{r} is a subspace of E^{s}_{σ} for s<0. Let s<0 and σ>-1/2 (σ>0) for the nonlocal NLS (for the nonlocal derivative NLS). We show the global existence and uniqueness of the solutions if the initial data belong to E^{s}_{σ} and their Fourier transforms are supported in (0,∞), the smallness conditions on the initial data in E^{s}_{σ} are not required for the global solutions.
报告3摘要：在这个报告中, 将介绍最近我们有关二维稳态磁流体方程组(MHD)在区域(0,L)×(0,∞)上的Prandtl边界层展开的稳定性(收敛性)结果. 物理边界为y=0, 该边界在水平方向上有一个常数为 u_{b}>0 的运动速度. 于是, 对于外流是剪切流或非剪切流的情形，我们得到x方向局部的稳定性结果. 对外流是简单的剪切流 (1,0,σ,0) 的情形, 我们得到了x方向的整体稳定性结果. 本报告的三个结果是和上海交通大学谢峰教授、华南师范大学林植林博士(现为北京大学愽士后)、纪志君愽士生合作完成的.
报告4摘要：This paper deals with a diffusive predator-prey chemostat system which describes the growth of planktonic rotifers, feeding on unicellular green algae. The dynamical behavior of this system is established in terms of the diffusion rate. The results show that there exist two critical diffusion rates which classify the dynamical behavior of this system into the following three scenarios: (i) for large diffusion rate, all species will be washed out; (ii) for an intermediate diffusion rate, the predator goes extinct and the prey survives; (iii) for relatively small diffusion rate, all species coexist.
报告5摘要：In this talk, we proposed the idea of combining the generalized variable separation method with the extended homoclinic test technique for solving higher-dimensional nonlinear evolution equations. We show the advantages of this method by solving (2+1)-dimensional breaking soliton equations. Abundant non-traveling exact solutions of the (2+1)-dimensional breaking soliton equation are obtained with the help of symbolic computation. These solutions obtained in this paper contain three arbitrary functions f(t); g(t); and Σ(t). As far as the author's knowledge, the solutions contain three arbitrary functions f(t); g(t); and Σ(t) have never been reported in the literature. Our results greatly enrich and expand the existing results. The results fully reveal the complexity of the solution structure of (2+1) dimensional breaking soliton equation. The previous results obtained in literatures can be regarded as special cases here. When some arbitrary functions included in these solutions are taken as some special functions, exact periodic solitary wave, cross soliton-like wave, periodic cross-kink wave, periodic two-solitary wave are presented. It is worth noting that the (3+1)-dimensional potential-YTSF equation and a new (2+1)-dimensional KdV equation can also be treated by this idea presented here.
报告6摘要：The global well-posedness the initial-boundary value problem on incompressible Navier-Stokes equations and the related models in the domain with the boundary is studied. The global existence of a new class of weak solution to the initial boundary value problem to two/three-dimensional incompressible Navier-Stokes equation with the pressure-velocity relation at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case is also established. Some extends to the corresponding incompressible fluid models such as Boussinesq equation and FSI models etc. are given.
报告7摘要：In this talk, the dyadic modified inhomogeneous and modified homogeneous energies are introduced. We will use these modified energies to consider the dispersive limit of the one dimensional fourth order Schrödinger equation: u_{t}+iεu_{xxxx}+i u_{xx}=(|u|^{2}u)_{x}, (t,x)∈R×R, ε∈R, and show that the solution of the fourth order Schrödinger equation converges in C(0,∞;H^{1}) to the solution of the derivative nonlinear Schrödinger equation: u_{t}+i u_{xx}=(|u|^{2}u)_{x} as ε tends to zero.
报告8摘要：In this talk, we give some results on the attractors of primitive equations 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.
报告9摘要：In this talk, we consider the quasi-neutral limit, zero-viscosity limit and vanishing capillarity limit for the compressible Navier-Stokes-Poisson system of Korteweg type in the half-space. The system is supplemented with the Neumann, Navier-slip and Dirichlet boundary conditions for density, velocity and electric potential, respectively. The stability of the approximation solutions involving the boundary layer is established by a conormal energy estimate, and then the convergence of solution of the Navier-Stokes-Poisson-Korteweg system to that of the compressible Euler equation is obtained with convergence rate.
报告10摘要：We consider the equations describing the interactions between Langmuir waves and the low-frequency 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.
报告11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 method, we prove the local well-posedness of IBVP in the Sobolev space H^{s}(R^{+}) for any s≥0 , and then we obtain the global well-posedness 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 iγ(|u|^{2u})_{x} and |u|^{2u} are taken into consideration.
第二分会场报告摘要
报告1摘要：This talk considers three-dimensional traveling surface waves on water of finite depth under the forces of gravity and surface tension using the exact governing equations, also called Euler equations. It was known that when two non-dimensional constants $b$ and $\lambda$, which are related to the surface-tension coefficient and the traveling wave speed, respectively, near a critical curve in the $(b, \lambda)$-plane, the Euler equations have a three-dimensional (3D) solution that has one hump at the center, approaches nonzero oscillations at infinity in the propagation direction, and is periodic in the transverse direction. We prove that in this parameter region, the Euler equations also have a 3D two-hump solution with similar properties. These two humps in the propagation direction are far apart and connected by small oscillations in the middle. The result obtained here is the first rigorous proof on the existence of 3D multi-hump water waves. The main idea of the proof is to find appropriate free constants and derive the necessary estimates of the solutions for the Euler equations in terms of those free constants so that two 3D one-hump solutions that are far apart can be successfully matched in the middle to form a 3D two-hump solution if some values of those constants are specified from matching conditions. The idea may also be applied to study the existence of 3D $2^n$-hump water-waves.
报告2摘要：Dispersive blow-up has being called to the development of point singularities due to the focusing of short or long waves. In this report, we show that the existence of dispersive blow up is provided by the linear dispersive solution and the integral nonlinear term is smoother than the free propagator term by at least sixth derivative in Sobolev space. This result will improve the previous result which was obtained in weighted Sobolev space.
报告3摘要：Exact solutions of higher-dimensional nonlinear equations takes a major place in the study of nonlinear phenomena observed in nature. In this article, some new kink type solutions are investigated for the new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP) equation. Firstly, a variety of solutions are obtained by Hirota's bilinear form, which include kink type wave solution, periodic solitary wave solutions and singular solitary wave solutions using extended homoclinic test approach. Secondly, solutions with three wave form are obtained by generalized three wave method. The extended homoclinic test approach is also used to construct solutions with a tail which explain some physical phenomenon.
报告4摘要：In this talk, firstly we shall introduce existence and asymptotic behavior of ground state results in the whole space R3 for quasilinear Schrödinger-Poisson systems when the nonlinearity coefficient ε> 0 goes to zero, where nonlinearity f(t) is asymptotically linear with respect to $t$ at infinity. Subsequently, for Schrödinger-Poisson systems with asymptotically linear or asymptotically 3-linear nonlinearity f(t), we give the results of the existence of two positive solutions by using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.
报告5摘要：In this talk, we investigate the finite volume method (FVM) for a distributed-order spacefractional advection-diffusion (AD) equation. The mid-point quadrature rule is used to approximate the distributed-order equation by a multi-term fractional model. Next, the transformed multi-term 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 second-order accuracy.
报告6摘要：This talk is concerned with a 3D Burgers equation perturbed by a linear multiplicative noise. Utilising Doss-Sussman transformation, we link the 3D stochastic Burgers equation to a 3D random Burgers equation. Utilising certain techniques from nonlinear partial differential equations and stochastic analysis, we are able to establish the global well-posedness of 3D Burgers equation with constant diffusion coefficient. Moreover, by developing a solution which is orthogonal to the gradient of diffusion coefficient, we extend the global well-posedness result to a more general case to allow the diffusion coefficient to be a function of space and time variables. Our results and methodology pave a way to extend regularity results of 1D Burgers equations to 3D Burgers equations. This talk is based on joint work with Zhao Dong (Chinese Academy of Sciences) and Guoli Zhou (Chongqing University).
报告7摘要：In this talk, we will introduce the recent results about the nonlinear stability of a shear layer profile for Navier Stokes equations near a boundary. This question plays a major role in the study of the inviscid limit of Navier Stokes equations in a bounded domain as the viscosity goes to 0. We mainly study the effect of cubic interactions on the growth of the linear instability here. In the case of the exponential profile and Blasius profile we obtain that the nonlinearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude O(μ^{1/4}) only, forming small rolls in the critical layer near the boundary. This is based on joint works with E. Grenier.