On statistical solutions for systems of conservation laws (talk cancelled)

Abstract: Entropy solutions are widely considered to be the suitable solution framework for multi-dimensional systems of conservation laws. However, recent results demonstrate that entropy solutions are not unique. Moreover, we show that many popular numerical methods do not converge to entropy solutions. Recently, we have proposed a notion of statistical solutions for systems of conservation laws. Statistical solutions are time-parameterized probability measures on spaces of integrable functions, whose moments satisfy an underlying infinite system of PDEs. In this talk, we will describe statistical solutions and some results on their existence, uniqueness and numerical approximation.