※このページは北大数学COEで作成しています
第15回諸分野のための数学研究会 (北大数学COE協賛)
Seminar on Mathematics for various disciplines
Program
- 日 時:
- 2007年4月12日(木) 16:30-17:30
- 場 所:
- 東京大学大学院 数理科学研究科056号室
※会場へのアクセスは下記にてご確認下さい。
駒場アクセスマップ
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
駒場キャンパス数理科学研究科棟
http://www.u-tokyo.ac.jp/campusmap/cam02_01_27_j.html
- 組織委員:
- 石村直之 (一橋大学)
儀我美一 (東京大学/北海道大学)
- プログラム:
-
- Boris Khesin(University of Toront)
- Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability.
- ABSTRACT:
- We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.
Further, we consider the non-holonomic optimal transport problem, related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.