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A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains
Abstract
For any γ∈ [ 0,1/3 ), we construct γ-Hölder-continuous martingale solutions to the two-dimensional stochastic incompressible Euler equations. These martingale solutions exhibit dissipative behavior and intermittency, thereby establishing the flexible part of the intermittent Onsager theorem. The proof rests on a stochastic and intermittent variant of the Newton--Nash iteration combined with the Littlewood--Paley decomposition scheme. This composite iteration scheme incorporates new stochastic pressure, Reynolds stress and intermittent perturbations to formalize the stochastic and intermittent fluctuations.
Related
- The L3-based strong Onsager theorem
- An Onsager-type theorem for SQG equations
- An Onsager-type theorem for the compressible Euler equations
- On the Onsager--Machlup functional of the infinite-dimensional angular central Gaussian distribution and related measures
- An Anisotropic Onsager Criterion for the Two-Dimensional Navier--Stokes Equations with Horizontal Viscosity
BibTeX
@misc{liu2026stochastic,
title = {{A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains}},
author = {Zhenxin Liu and Wenhu Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30582},
eprint = {2608.30582},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30582},
}
RIS
TY - UNPB
TI - A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains
AU - Zhenxin Liu
AU - Wenhu Zhong
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.30582
UR - https://arxiv.org/abs/2608.30582
AB - For any γ∈ [ 0,1/3 ), we construct γ-Hölder-continuous martingale solutions to the two-dimensional stochastic incompressible Euler equations. These martingale solutions exhibit dissipative behavior and intermittency, thereby establishing the flexible part of the intermittent Onsager theorem. The proof rests on a stochastic and intermittent variant of the Newton--Nash iteration combined with the Littlewood--Paley decomposition scheme. This composite iteration scheme incorporates new stochastic pressure, Reynolds stress and intermittent perturbations to formalize the stochastic and intermittent fluctuations.
ER -