2022世界青年科学家峰会——数学及其应用前沿论坛，将于10月21-24日在温州召开。本次论坛由三个分论坛构成：图论与组合数学分论坛、基础数学分论坛与应用数学分论坛。10月13日，据论坛筹备组消息，应用数学分论坛已完成议程安排工作，初步如下：

欢迎关注本次分论坛活动，附《Title and Abstract》。

 

Invariant Geometric Flows and Integrable Systemsin Affine-related Geometries

 

(Prof. Changzheng Qu 屈长征教授 宁波大学)

 

Abstract: It is well-known that integrable systems are related to invariant geometric flows in certain geometries. In this talk, we are mainly concerned with invariant geometric flows in affine- related geometries including centro-equiaffine, centro-affine, affine and affine-symplectic geometries. First, we show that the specific invariant geometric flows in those geometries are related respectively to the well-known integrable systems. Second, the geometric formulations to integrability features of the resulting systems are investigated. Third, the geometric formulations of Miura-transformation and its various extensions are also investigated. This talk is based on the works joint with Peter Olver, Kaiseng Chou, Yun Yang and Zhiwei Wu.

 

 

  Hilbert expansion for kinetic equations with non-relativistic Coulomb collision

( Huijiang Zhao 武汉大学)

 

Abstract: This talk is concerned with the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is to give a rigorous derivation of the compressible Euler equations from the Landau equation via the Hilbert expansion; while the second one is to prove, still in the setting of Hilbert expansion, that the unique classical solution of the Vlasov-Maxwell-Landau system converges, which is shown to be globally in time, to the resulting global smooth solution of the Euler-Maxwell system, as the Knudsen number goes to zero. The main ingredient of our analysis is to derive some novel interplay energy estimates on the solutions of the Landau equation and the Vlasov-Maxwell-Landau system which are small perturbations of both a local Maxwellian and a global Maxwellian, respectively

 

 

Mathematical computations of peristaltic nanofluids and blood 

flows in stenosed arteries

(Prof. Sohail Nadeem  巴基斯坦真纳大学  院士)

 

Abstract: The talk has two portions thus two abstracts are given below

1. A mathematical model is presented to analyse the flow characteristics and heat transfer aspects of a heated Newtonian viscous fluid with single wall carbon nanotubes inside a vertical duct having elliptic cross section and sinusoidally fluctuating walls. Exact mathematical computations are performed to get temperature, velocity and pressure gradient expressions. A polynomial solution technique is utilized to obtain these mathematical solutions. Finally, these computational results are presented graphically and different characteristics of peristaltic flow phenomenon are examined in detail through these graphs. The velocity declines as the volume fraction of carbon nanotubes increases in the base fluid. Since the velocity of fluid is dependent on its temperature in this study case and temperature decreases with increasing volumetric fraction of carbon nanotubes. Thus velocity also declines for increasing volumetric fraction of nanoparticles.

2. This research culminates the arterial blood flow analysis through distinct stenotic regions. Four different forms of stenotic regions are woven together in present study, i.e. triangular, trapezoidal, overlapping (w-shape) and composite formations. The four reviewed stenotic formations are first time considered in such numerical analysis. The considered problem is modeled for an elliptical cross-sectional artery by means of a cartesian coordinate system. The governing coupled Partial differential equations are decoded numerically over this elliptical cross-section by using free source CFD software Open-FOAM. A precisely refined and proper mesh is generated for each arterial stenotic segment. A high magnitude of flow profile with some minor disruptions is observed near the origin of stenotic sections of artery. Pressure profile also has high values near the sharp corners of stenotic regions. Some expected irregularities in the flow profile are observed near the origin of stenotic regions as it happens in most real-life stenosed artery blood flow problems.

 

 

Perspectives on Stochastic Dynamics and Data Science

 (Prof. Jinqiao Duan 段金桥教授 伊利诺伊理工学院，高婷教授 华中科技大学数学中心)

 

Abstract: The speakers will present some recent advances in stochastic dynamics, and the interactions with data science. One focus is on stochastic dynamical tools for data-driven modeling and prediction, while the other focus is on data science methods for understanding stochastic dynamics.

 

 

Almost sure scattering for the nonlinear Schrodinger equation

( Prof. Yifei Wu   吴奕飞教授 天津大学)

 

Abstract: In this talk, I will present a recent work about the almost sure scattering for the non-radial defocusing non-linear Schrodinger equations, including the energy-critical case, energy-subcritical case and mass-critical case. This is finished joint with Jia Shen and Avy Soffer. Previously, in the energy critical case, there is no probabilistic global large data result for 3D NLS, and all the known probabilistic scattering results in 4D case require the initial data in H^s with some s>0. As one of our result, we proved the scattering for 3D and 4D defocusing energy critical NLS for almost all the non-radial data in H^s with any s in R. In particular, our result does not rely on any spherical symmetry, size or regularity restrictions.

 

Inertial manifolds for some dissipative systems

(Prof. Chunyou Sun  孙春友教授 兰州大学)

Abstract:This talk will focus on our recent works about the existence of inertial manifolds for several dissipative systems, including a simple singularly non-autonomous model and the complex Ginzburg-Landau equations. This is a joint work with A.Kostianko, Xinhua Li, and S.Zelik.

 

 

 

Global well-posedness for the compressible viscous non-resistive MHD system

(Prof. Yongsheng Li and Xiaoping Zhai  李用声、翟小平教授 华南理工大学、广东工业大学)

 

Abstract: How to  construct the global  small solutions to the  compressible viscous non-resistive MHD system in  $\mathbb{R}^3$ is  an open problem. In the report, I will  present some recent processes about this problem.

 

 

Near Optimality of Stochastic Control for Singularly

Perturbed McKean-Vlasov Systems

(Fuke Wu  吴付科教授 华中科技大学)

 

Abstract: In this paper, we are concern with the optimal control problems for a class of systems with fast-slow processes. The problem under consideration is to minimize a functional subject to a system described by two-time scaled McKean-Vlasov stochastic differential equation whose coefficients depend on state components and their probability distributions. Firstly, we establish the existence and uniqueness of the invariant probability measure for the fast process. Then, by using the relaxed control representation and the martingale method, we prove the weak convergence of the slow process and control process in the original problem, and obtain an associated limit problem in which the coefficients are determined by the average of those of the original problem with respect to the invariant probability measure. Finally, by establishing the nearly optimal control of the limit problem, we obtain the near optimality of the original problem.

 

 

The Cauchy problem for the generalized ZK equation

( Prof. Wei Yan  闫威教授 河南师范大学)

 

Abstract: In this paper, we consider the two-dimensional generalized Z-K equation

\begin{eqnarray}&&u_{t}+\partial_{x}(\Deltau)=\frac{1}{k+1}(u^{k+1})_{x},\label{1.01}\end{eqnarray}where $k\geq2$, $u=u(x,y,t)$ is a real valued function.  By establishing some new Strchartz estimates, we establish some bilinear estimates and trilinear estimates as well as some multilinear estimates and improve some well-posedness results. We also investigate pointwise convergence and uniform convergence.