Évènement

The celebrated method of DiPerna and Majda guarantees energy conservation for an important class of weak solutions to 2D Euler Equations with vortex sheet initial data provided that its circulation maximal function has log-decay rate strictly larger than 1. On the other hand, well-known constructions exhibit the concentration-cancellation phenomenon under the slightly weaker assumption that circulation maximal function has log-decay of order 1/2. Then the DiPerna-Majda gap problem asks: concentration-cancellation vs. energy conservation in the remaining log-range (1/2,1]?

In this talk, after reviewing earlier contributions to the DiPerna-Majda gap problem, I will present a new approach to this question based on sparseness. This is based on joint projects with M. Milman and D. Spector.