题目：Constructing two-dimensional optimal system of the group invariant solutions

报告人：陈勇  （华东师范大学）

时间： 2018年11月28日（周三） 上午 10：00－11：00

地点： 教学楼A308

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.

报告人简介：

陈勇，华东师范大学，教授，博士生导师，计算机理论研究所所长，上海市闵行区拔尖人才，卓越教授岗位。长期从事非线性物理、可积系统、混沌理论、符号计算、大气和海洋动力学和数值计算等领域的研究工作。陈勇教授提出了一系列可以机械化实现可积理论的研究方法，建立了非线性工程系统平台，发展了李群理论并成功应用于大气海洋物理模型的研究，并在非局域对称和对称优化理论，怪波理论和混沌理论中提出了一系列方法。陈勇教授主持和参与了包括国家自然科学基金重点项目、国家自然科学基金面上项目、973全球变化研究国家重大科学研究计划项目、博士点基金项目、国家自然科学基金创新群体等多项国家级科研项目。陈勇教授已在SCI收录的国际学术期刊上发表论文260余篇，发表论文的SCI他引3000余次。