报告题目：Constructing two-dimensional optimal system of the group invariant solutions
报告时间：2018年11月8日（周四）上午9点
报告地点：理学院二楼会议室
报告人简介：陈勇，华东师范大学教授、博士生导师，主要从事非线性数学物理、可积系统、计算机符号计算和程序开发的研究；主持和参与国家自然科学基金面上项目、博士点基金、两次国家基金委重点项目基金、连续两届国家自然科学基金创新群体基金（项目骨干成员）、国家重大科学研究计划项目（973）等项目（骨干科学家）。
报告摘要：To search for inequivalent group invariant solutions of two-dimensional optimal system, a direct and systematic approach is established, which is based on commutator relations, adjoint matrix, and the invariants. The details of computing all the invariants for two-dimensional algebra are presented, which is shown more complex than that of one-dimensional algebra. The optimality of two-dimensional optimal systems is shown clearly for each step of the algorithm, with no further proof. To leave the algorithm clear, each stage is illustrated with a couple of examples: the heat equation and the Novikov equation. Finally, two-dimensional optimal system of the (2+1) dimensional Navier-Stokes (NS) equation is found and used to generate intrinsically different reduced ordinary differential equations. Some interesting explicit solutions of the NS equation are provided.