2026/03/12 by Marco Bagnara, Daniel W. Boutros, Camillo De Lellis +1 · 1 citation
#math.AP #math.PR
We prove the absence of anomalous dissipation for passive scalars driven by some random autonomous divergence-free vector fields in \mathbb Td. In dimension d=2 we just need continuity almost surely and a mild nondegeneracy condition on the randomness. In dimension d≥ 3 we assume a special geometric structure and almost sure Hölder regularity with a Hölder exponent bigger than (1)/(8). No regularity is assumed on the passive scalar except for boundedness in the initial data. The proof relies on dimension-theoretic arguments, as opposed to commutator estimates. A consequence of these results is that the same assumptions prevent (almost surely) many other expected properties of turbulent flows, such as anomalous regularization, the Yaglom-Obukhov-Corrsin law, and Richardson diffusion.