Analysis and Mathematical Physics

We give several constraints on the dissipation measure arising in the inviscid limit of two-dimensional incompressible fluids under minimal assumptions on the initial datum. None of them is replicable in three dimensions, highlighting the non-trivial effect of the higher order conserved quantity, or "double cascade", even in regularity settings where it shouldn't be that effective. When "scales are quantified", we are able to provide new criteria for anomalous dissipation. There is reason to believe that this is part of a more general picture.