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arXiv · 2606.28575

Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations

Antonio Agresti·Federico Butori·Eliseo Luongo
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Abstract

We study a logarithmically hyperviscous Navier-Stokes model on the three-dimensional torus with Lie-transport noise, which includes both transport and stretching. We prove that, for noise of sufficiently large intensity and high frequency, the system admits a unique global smooth solution with probability arbitrarily close to one. Unlike previous works, this physically motivated noise does not preserve energy or enstrophy, but rather circulation. Global well-posedness is established through a probabilistic mechanism that produces effective dissipation via a scaling limit. Crucially, this approach bypasses the lack of conserved quantities and tames the singular nature of stochastic stretching.

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BibTeXRIS

Antonio Agresti, Federico Butori, Eliseo Luongo. 2026-06-26. Global smooth solutions by high mode Lie-Transport noise for Logarithmically Hyperdissipative Navier-Stokes equations. https://arxiv.org/abs/2606.28575

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