**On
variational formulation of entropy
solutions to nonlinear conservation laws**

Eitan
Tadmor

and

Abstract:

A
proper notion of weak solutions for nonlinear conservation laws
requires such
solutions to be *entropic*. Entropy solutions are found to
be at the
crossroads, when reached from a microscopic description of
kinetic formulation
or from a macroscopic description as vanishing viscosity limits.
In both cases,
entropy solutions were also interpreted within a proper
variational framework.

The
notion
of entropy, which is intimately connected with symmetry, is an
extension
*imposed* on nonlinear systems conservation laws. In this
context, K. O.
Friedrichs in his 1979 John von Neumann Lecture, asked

“*Now,
in
many branches of physics … symmetries play a fundamental role,
but all these
symmetries—as it seems to me—are assumed and not derived. I
now wonder whether
or not … symmetries can also be derived*.”

In
this
lecture I will give a concise overview on the theory and
computation of entropy
solutions for nonlinear conservation laws, and I will present a
new variational
formulation which addresses the question raised by Friedrichs.