Recently there has been considerable research into the stability of shocks in systems of conservation laws, with stability understood in some square-integrable sense. In this talk I will give some background on systems of nonlinear hyperbolic partial differential equations (known as conservation laws), and on the issues concerning well-posedness. There are reasons that the still-unsolved problem of existence of solutions in more than a single space dimension is expected to involve L-2. We present a simple, rather discouraging, example that shows why that goal seems elusive. This is joint work with Hao Ying.

Zoom meeting: Link