Analysis Seminar: On a Hamilton-Jacobi theory for Hydrodynamic limit of action minimizing collective dynamics

Abstract: In this joint work with Toshio Mikami from Tsuda University, we examine a class of multi-scale limit theorems for Hamilton-Jacobi equations defined in space of probability measures. We rely upon versions of abstract viscosity solution, as well as variational arguments, to study problems about (global) action minimizing collective Hamiltonian dynamics.
Our tools are mainly mass transport calculus, finite dimensional weak KAM (Kolmogorov- Arnold-Moser) theory, and viscosity solution theory for Hamilton-Jacobi equations in space of probability measures (studied using first order calculus in Alexandrov metric spaces).

Host: Xiang Tang