2025/02/14 by Luigi De Rosa, Theodore D. Drivas, De Rosa, Luigi +5 · 2 citations
Engineering · #Fluid Dynamics and Turbulent Flows #math-ph #math.AP #math.MP #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2502.10032
openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 optimal 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.