Measure-Valued Solutions of the Euler Equations

Measure-valued solutions of the incompressible Euler equations were first considered by DiPerna and Majda to describe effects of oscillation and concentration in ideal fluids. Although measure-valued solutions appear a priori as much weaker objects than distributional solutions, we have been able to show that both notions are in a sense equivalent. An important open question concerns the relation between weak and measure-valued solutions for compressible Euler models. Joint work with L. Székelyhidi, Jr.