題目一：A remark on the generalized Toscani metric
内容簡介：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.
報告人：日本京都大學數學系 Yoshinori Morimoto 教授
報告人簡介：Yoshinori Morimoto 教授1999年4月起任日本京都大學數學系教授，2016年4月開始任京都大學Emeritus Professor(榮譽教授)。他是國際知名的微局部分析和Boltzmann方程研究專家。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等國際著名雜志發表了一批高水平的論文。由于他在“亞橢圓算子和不帶角截斷的Boltzmann方程數學理論”方面的貢獻，Yoshinori Morimoto教授2011年9月獲得日本數學會“分析類獎(Analysis Prize by Japan Mathematical Society)”。
時 間：2017年1月15日（周日）上午10：00始
題目二：Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids
内容簡介：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 $/bbt^2:=/bbr^2//bbz^2$.
報告人：中科院武漢物理與數學研究所 肖清華 副研究員
報告人簡介：肖清華博士畢業于武漢大學，現為中科院武漢物理與數學研究所副研究員，研究生導師。主要從事非線性偏微分方程的研究，在Boltzmann方程和與Cucker Smale 方程相關的動力學解的适定性與雙曲型偏微分方程波的穩定性方面做了一系列的工作，在 JFA，SIAM J.Math.Anal, J. Stat. Phys., J. Differential Equations 等國際著名期刊上發表論文近20篇。
時 間：2017年1月15日（周日）上午10：40始
題目三：Global well-posedness of the Boltzmann equation with large amplitude initial data
内容簡介：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
報告人：中國科學院數學與系統科學研究院 王勇 博士
報告人簡介：王勇本科畢業于湖南師範大學，博士畢業于中國科學院數學與系統科學研究院，主要從事非線性偏微分方程的研究，在Boltzmann方程的适定性、流體動力學極限以及Navier-Stokes方程的粘性消失極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.等國際著名雜志發表論文近20篇。
時 間：2017年1月15日（周日）上午11：20始
地 點：南海樓224室
熱烈歡迎廣大師生參加!
太阳集团1088vip/網絡空間安全學院
2017年1月12日