A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Liu, Zhenxin, Zhong, Wenhu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G322682455, G4060397366, G522012478
OpenAlex ID: W7204934849