Higher dimensional affine fluids and geodesics of SL(n)
主讲人:Willie Wong( Michigan State University) 
活动地址:腾讯会议 ID: 496 250 906  

Abstract: One way to understand incompressible fluids is to regard it as constrained free particle transport, a point of view realized in the Euler-Arnol'd formulation of fluid flow as a geodesic motion on the volume-preserving diffeomorphism group. In this talk we will discuss some observations that grew out of the further restriction that the fluid flow be affine. Sideris (2017) observed that such affine fluid flows can be described as geodesics on SL(n) with the Hilbert-Schmidt metric, and studied the properties of several explicit solutions when n = 3. Roberts, Shkoller, and Sideris (2020) then integrated the geodesic equations when n = 2 and obtained a complete classification. In this talk I will present some contrasting results obtained, in collaboration with my students Audrey Rosevear and Samuel Sottile, concerning the geodesic geometry of SL(n) for n > 2, and their applications towards stability and instability of the free boundary incompressible Euler flow.

前沿课程 | 广西数学研究中心2023年研究生前沿课程招生简章
前沿课程 | 广西数学研究中心2022年研究生前沿课程录取名单