Isospectral flows for shock clustering and Burgers turbulence

Luen-Chau Li (Penn State University) , IS Seminar Series

In recent work, Menon and Srinivasan showed that the study of scalar 
hyperbolic conservation laws with a certain class of random  initial 
conditions give rise to isospectral flows.   

In this talk, I will describe progress made in understanding these Lax equations 
in the last few years. In particular, I will show that if the initial process is 
a pure-jump Markov process which can only assume a finite number of states, the 
flow is conjugate to a straight line motion, and the equation is exactly solvable.