back Back to all Seminars

AMCS Seminar | Euler sprays and optimal transportation

Start Date: March 16, 2016
End Date: March 16, 2016

By Professor Jian-Guo Liu ( Duke University )

Just as Captian James T. Kirk said, “Beam me up, Scotty!”, optimal transportation between two bounded open sets in R^d with equal volume can be realized as an Euler spray consisting a countable superposition of ellipsoidal droplet solutions of incompressible Euler equations (water wave equation). Every Wasserstein geodesic between shape densities is a weak limit of a sequence of weak solutions 
of the incompressible Euler equations. We further exhibit a fascinating connection between Wasserstein geodesics and work of Brenier on relaxations of Arnold's least-action principle for incompressible flow. Each Wasserstein geodesic is also the unique minimizer of a relaxed least-action principle for a fluid-vacuum mixture. This is a joint work with Bob Pego and Dejan Slepcev of Carnegie Mellon University, USA.

Jian-Guo Liu obtained his BS in Mathematics from Fudan University in Shanghai in 1982 and a PhD in Mathematics from UCLA in 1990. He was a postdoc at Courant Institute 1990-1993, an assistant professor at Temple University 1993-1997, an associate professor, then a professor at University of Maryland 1997-2009. He moved to Duke University as a professor of mathematics and physics in 2009. Liu’s research is in the areas of nonlinear PDE, collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences; scaling behavior in models of clustering and coarsening; numerical methods for incompressible viscous flow; and multiscale analysis and computation.

More Information:

For more info contact: Professor Peter A. Markowich; email:

Date: Wednesday 16th March 2016
Time: 15:00 - 14:00
Location: Building 1, Level 4 Room 4214
Refreshmentswill be available at 14:45