Mathematics for various disciplines Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
 Date

20070412 16:30 
20070412 17:30
 Place
 Graduate School of Mathematical Sciences the University of Tokyo, Room #056

Speaker/Organizer
 Boris Khesin （University of Toront）

 We describe a simple relation between curvatures of the group of volumepreserving diffeomorphisms (responsible for Lagrangian instability of idealfluids via Arnold's approach) and the generation of shocks for potentialsolutions of the inviscid Burgers equation (important in mass transport). For this we characterize focal points of the group of volumepreservingdiffeomorphism, regarded as a submanifold in all diffeomorphisms and thecorresponding conjugate points along geodesics in the Wasserstein space ofdensities. Further, we consider the nonholonomic optimal transport problem, related to the following nonholonomic version of the classical Moser theorem: given abracketgenerating distribution on a manifold two volume forms of equal totalvolume can be isotoped by the flow of a vector field tangent to this distribution.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index_en.html