Intermittency and Dissipation Regularity in Turbulence
Analysis of PDEs
2025-02-19 v1 Mathematical Physics
math.MP
Fluid Dynamics
Abstract
We lay down a geometric-analytic framework to capture properties of energy dissipation within weak solutions to the incompressible Euler equations. For solutions with spatial Besov regularity, it is proved that the Duchon-Robert distribution has improved regularity in a negative Besov space and, in the case it is a Radon measure, it is absolutely continuous with respect to a suitable Hausdorff measure. This imposes quantitative constraints on the dimension of the, possibly fractal, dissipative set and the admissible structure functions exponents, relating to the phenomenon of "intermittency" in turbulence. As a by-product of the approach, we also recover many known "Onsager singularity" type results.
Cite
@article{arxiv.2502.10032,
title = {Intermittency and Dissipation Regularity in Turbulence},
author = {Luigi De Rosa and Theodore D. Drivas and Marco Inversi and Philip Isett},
journal= {arXiv preprint arXiv:2502.10032},
year = {2025}
}