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arXiv · 2608.30582

A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains

Zhenxin Liu·Wenhu Zhong
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Abstract

For any $γ\in \left[ {0,\frac{1}{3}} \right)$, 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.

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Zhenxin Liu, Wenhu Zhong. 2026-09-14. A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains. https://arxiv.org/abs/2608.30582

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