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arXiv · 2511.21616

Dissipative solutions to randomly forced 3D Euler equations

Umberto Pappalettera·Francesco Triggiano
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Abstract

The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states.

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Umberto Pappalettera, Francesco Triggiano. 2026-03-05. Dissipative solutions to randomly forced 3D Euler equations. https://arxiv.org/abs/2511.21616

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