题目一：A remark on the generalized Toscani metric

内容简介：From the middle of 1990s, Toscani and his coauthors, analytically, studied the existence, the uniqueness and the asymptotic behavior of solutions to the Cauchy problem for the non cutoff spatially homogeneous Boltzmann equation of Maxwellian molecules, introducing the so-called Toscani metric defined in the space of the Fourier image of probability measures, motivated by an earlier work of H. Tanaka (1978) by means of the probabilistic method. Inspired by the research of Cannone-Karch(2010) on the infinite energy solutions to the above Cauchy problem，(including self-similar solutions of Bobylev-Cercignani) by means of Toscani metric, the generalization of Toscani metric has been discussed in a series of joint works with Shuaikun Wang and Tong Yang. Furthermore, in a recent paper (SIAM J. M. A. 2016) by Yong-Kum Cho and us, the class of probability measures possessing finite moments of an arbitrary positive order is characterized in terms of the symmetric difference operators of their Fourier transforms. In this talk, I review this generalization of Toscani metric and give a supplementary remark on the equivalence between the generalized Toscani metric and the Monge-Kantorovich metric.

报告人：日本京都大学数学系  Yoshinori Morimoto  教授

报告人简介：Yoshinori Morimoto 教授1999年4月起任日本京都大学数学系教授，2016年4月开始任京都大学Emeritus Professor(荣誉教授)。他是国际知名的微局部分析和Boltzmann方程研究专家。在Archive for Rational Mechanics and Analysis、Communications in Mathematical Physics、Journal of Differential Equations、Journal of the European Mathematical Society、Journal of Functional Analysis、Journal de Mathématiques Pures et Appliquées等国际著名杂志发表了一批高水平的论文。由于他在“亚椭圆算子和不带角截断的Boltzmann方程数学理论”方面的贡献，Yoshinori Morimoto教授2011年9月获得日本数学会“分析类奖(Analysis Prize by Japan Mathematical Society)”。

时  间：2017年1月15日（周日）上午10：00始

题目二：Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

内容简介：We study the dynamics of  infinitely many Cucker-Smale(C-S) flocking particles under the interplay of a random communication and incompressible fluid. For the dynamics of ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion coefficient, whereas for the fluid part, we use the incompressible Navier-Stokes(N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present global existence of weak and strong solutions in $/bbr^d $ $(d=2 or 3)$. Under extra regularity assumptions of initial data, the unique solvability of strong solutions is also established in $/bbr^2$. In a large coupling regime and a periodic spatial domain, we show that the velocities of C-S particles and fluids are asymptotically aligned to constant velocities in a two-dimensional periodic spatial domain $/bbt^2:=/bbr^2//bbz^2$.

报告人：中科院武汉物理与数学研究所  肖清华  副研究员

报告人简介：肖清华博士毕业于武汉大学，现为中科院武汉物理与数学研究所副研究员，研究生导师。主要从事非线性偏微分方程的研究，在Boltzmann方程和与Cucker Smale 方程相关的动力学解的适定性与双曲型偏微分方程波的稳定性方面做了一系列的工作，在 JFA，SIAM J.Math.Anal,  J. Stat. Phys.,  J. Differential Equations 等国际著名期刊上发表论文近20篇。

时  间：2017年1月15日（周日）上午10：40始

题目三：Global well-posedness of the Boltzmann equation with large amplitude initial data

内容简介：The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^/infty_xL^1_{v}/cap L^/infty_{x,v}$  approach,   we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^/infty$ norm under some  smallness condition on $L^1_xL^/infty_v$ norm as well as  defect mass, energy and entropy so that the initial data  allow  large amplitude oscillations. Both the hard and  soft potentials with angular cut-off are  considered,  and the large time behavior of solutions in $L^/infty_{x,v}$ norm with explicit rates of convergence is also studied

报告人：中国科学院数学与系统科学研究院  王勇  博士

报告人简介：王勇本科毕业于湖南师范大学，博士毕业于中国科学院数学与系统科学研究院，主要从事非线性偏微分方程的研究，在Boltzmann方程的适定性、流体动力学极限以及Navier-Stokes方程的粘性消失极限等方面做了一系列的工作，在Archive for Rational Mechanics and Analysis、SIAM J. Math. Anal.、Journal of Differential Equations、Discrete Contin. Dyn. Syst.等国际著名杂志发表论文近20篇。

时  间：2017年1月15日（周日）上午11：20始

地  点：南海楼224室

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2017年1月12日