| The classic result of Beale, Kato, and Majda provides a rigorous connection between the growth of the velocity field of an incompressible, inviscid fluid and the associated vorticity. When we consider this phenomenon from the perspective of Littlewood-Paley theory, we see the potential blowup of the velocity of a fluid as being caused by a cascade of kinetic energy flowing to successively higher frequency scales. Using this heuristic, we present two results: one on the Navier-Stokes equations with a modified dissipation term and another regarding the possibility of such a frequency cascade in the two-dimensional Euler equations. |
