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arXiv · 2609.31369

Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise

Abhishek Chaudhary·Ujjwal Koley·Andreas Prohl
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Abstract

We study a fully discrete approximation theory for the two-dimensional incompressible Euler equations on $\mathbb{T}^{2}$, in vorticity form, driven by Kraichnan-type transport noise and with $\mathbb{H}^{-1}(\mathbb{T}^2)$-valued initial vorticity. The main new ingredient is a finite-dimensional coercivity estimate for the torus Kraichnan model, which captures at the discrete level the regularizing mechanism induced by the rough transport noise. Together with a new compactness strategy based on continuous equation-based interpolants and localized discrete estimates, this coercivity estimate gives tightness of the approximations and shows that subsequential limit is a weak martingale solution of the Euler equations.

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Abhishek Chaudhary, Ujjwal Koley, Andreas Prohl. 2026-09-25. Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise. https://arxiv.org/abs/2609.31369

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