Speaker:	陈勇教授，华东师范大学
Inviter:	胡星标研究员
Title:	Constructing two-dimensional optimal system of the group invariant solutions
Time & Venue:	2018.12.26 19:30-20:30 N210
Abstract:	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.

Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars