5月7日:范恩贵
发布时间:2018-04-28  阅读次数:1675

报告题目:The analytical solutions for the n-dimensional Boussinesq equations without viscosity

:范恩贵 教授

:陈勇教授

报告时间:201857日(周一)10:00-11:30

报告地点:中北校区数学馆东202

 

报告摘要:

In this paper, we construct two kinds of interesting explicit analytical solutions for n-dimensional Boussinesq equations without viscosity. The first kind is Cartesian linear analytical solutions with respect to velocity field u=(u_1, u_n), The first n-1 velocity field (u_1,, u_{n-1}) can be can be characterized by  a linear transformation of a matrix A with respect to coordinates of spital variables; while last velocity u_n is characterized by the trace of the matrix A; The pressure p and temperature \theta are related to the well-known heat equation. The technique used here is matrix and curve integration theory to transform analytically solving the n-dimensional Boussinesq equations into algebraically constructing an appropriate matrix. The second kind is nonlinear solutions with respect to velocity field u=(u_1,,u_n). The first n-1 velocity field (u_1,, u_{n-1}) can be can be characterized by the classical $(n-1)$-dimensional Laplace equation;  while the last velocity u_n is linear; The pressure p and temperature \theta are  characterized by a generalized heat equation with variable coefficient. The technique used here is multi-dimensional.

 

报告人简介:

复旦大学数学科学学院教授、博士生导师。研究方向:数学物理、Riemann-Hilbert方法、正交多项式和随机矩阵。近年来,连续二届为国家973课题成员、主持国家自然科学基金、上海曙光计划、上海曙光计划跟踪课题等多项研究课题。应邀访问美国密苏里大学、密西根州立大学、德克萨斯大学、波兰华沙大学、香港大学、香港城市大学、日本京都大学等。在国外重要刊物上发表论文100余篇所发表论文被SCI刊源他引3000余次。2002年,获上海市曙光学者称号;2007年,获上海市自然科学二等奖; 2008年,获国际汤姆森路透卓越研究奖、上海市曙光跟踪学者称号;2016年获教育部自然科学二等奖;2016年,获教育部自然科学二等奖;2017年,获谷超豪数学奖

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