integrability of shock clustering and Burgers turbulence.
Menon, Brown University
( joint work with Ravi
Srinivasan, UT, Austin)
The emergence of structure from disorder is interesting
in several physical models such as galaxy formation in astrophysics,
vortex coalecence in 2d flows, and domain growth in materials science.
One mathematical model for such phenomena is to study the equations of
continuum physics with random initial data.
We show that this
problem has a very rich structure even for the
simplest nonlinear equations. Our main result is that the evolution of
shock statistics for scalar conservation laws with convex flux and
suitable random data is completely integrable. These results sit
interesting junction of kinetic theory, integrable systems, and
probability theory. Little background will be presumed in any of these