PDE seminar by Ulrik Skre Fjordholm
Speaker: Ulrik Skre Fjordholm (UiO)
Title: Statistical solutions of hyperbolic conservation laws
Abstract: Recent theoretical and numerical results have shown that inviscid models in gas dynamics, such as the (in)compressible Euler equations, are unstable with respect to initial data or even ill-posed. Going back to the roots of turbulence theory, we interpret instead these hyperbolic conservation laws in a probabilistic manner. In this talk I will survey some recent developments in so-called statistical solutions, both theoretical and numerical. These include well-posedness for scalar conservation laws; energy conservation for regular solutions of the incompressible Euler equations; and numerical evidence for the convergence of the mean flow, structure functions etc. for the compressible Euler equations.