2025/10/13 by Fan, Louis Wai-Tong, Fan, Wai-Tong Louis, Ali Pakzad +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2510.12004
Due to the chaotic nature of turbulence, statistical quantities are often more informative than pointwise characterizations. In this work, we consider the stochastic Ladyzhenskaya-Smagorinsky equation driven by space-time Gaussian noise on a three-dimensional periodic domain. We derive a rigorous upper bound on the first moment of the energy dissipation rate and show that it remains finite in the vanishing viscosity limit, consistent with Kolmogorov's phenomenological theory. This estimate also agrees with classical results obtained for the Navier-Stokes equations and demonstrates that, in the absence of boundary layers, as considered here, the model does not over-dissipate.