A famous result ofDelort (1991) establishes the concentration-

cancellationphenomenon for approximating solutions of 2D Euler equations

with a vortex sheetwhose vorticity maximal function has a log-decay of order

1/2 . On the otherhand, DiPerna and Majda (1987) showed that if the log-

decay assumption isstrictly larger than 1 then the lack of concentration

(and hence energyconservation) holds. Then the so-called DiPerna-Majda

gap problem asks:concentration-cancellation vs. energy conservation in the

remaining log-range(1/2,1]?

In this talk, afterreviewing earlier contributions to the DiPerna-Majda

gap problem, I willpresent a new approach to this question based on sparse-

ness. This is based onjoint projects with Mario Milman and Daniel Spector.

The talk will beself-contained, and no additional prerequisites are needed.