An intriguing, and largely open, question in mathematical fluid dynamics is whether solutions of the Navier-Stokes equations converge in some sense to a solution of the Euler equations in the zero viscosity limit. In fact this convergence could conceivably fail due to oscillations and concentrations occuring in the sequence.
In the late 1980s, R. DiPerna and A. Majda extended the classical concept of Young measure to obtain a notion of measure-valued solution of the Euler equations, which records precisely these oscillation and concentration effects. In this talk I will present a result recently obtained in joint work with L. Székelyhidi, which states that any such measure-valued solution is generated by a sequence of distributional solutions of the Euler equations.
The result is interesting from two different viewpoints: On the one hand, it emphasizes the huge flexibility of the concept of weak solution for Euler; on the other hand, it provides an example of a characterization theorem for Young measures in the tradition of D. Kinderlehrer and P. Pedregal where the differential constraint on the generating sequence does not satisfy the constant rank condition.