報告題目👰♀️：Constructing two-dimensional optimal system of the group invariant solutions
報告時間😸：2018年11月8日（周四）上午9點
報告地點：必一体育平台二樓會議室
報告人簡介：陳勇，華東師範大學教授、博士生導師👷🏻♂️，主要從事非線性數學物理⏬、可積系統、計算機符號計算和程序開發的研究💁🏻♀️；主持和參與國家自然科學基金面上項目、博士點基金、兩次國家基金委重點項目基金👩🎤⚽️、連續兩屆國家自然科學基金創新群體基金（項目骨幹成員）、國家重大科學研究計劃項目（973）等項目（骨幹科學家）🤽🏻。
報告摘要：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.