Time-averaged statistics of the 3D stochastic Ladyzhenskaya-Smagorinsky equations

Fuente: arXiv
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Autori principali: Fan, Louis Wai-Tong, Pakzad, Ali
Natura: Preprint
Pubblicazione: 2025
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author Fan, Louis Wai-Tong
Pakzad, Ali
author_facet Fan, Louis Wai-Tong
Pakzad, Ali
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_12004
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Time-averaged statistics of the 3D stochastic Ladyzhenskaya-Smagorinsky equations
Fan, Louis Wai-Tong
Pakzad, Ali
Analysis of PDEs
Primary 35Q30, 76F55, 35R60, Secondary 35Q35
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.
title Time-averaged statistics of the 3D stochastic Ladyzhenskaya-Smagorinsky equations
topic Analysis of PDEs
Primary 35Q30, 76F55, 35R60, Secondary 35Q35
url https://arxiv.org/abs/2510.12004