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arXiv · 2609.24396

Well-posedness of a stochastic Navier-Stokes system with dynamically coupled subgrid scales

Arnaud Debussche·Etienne Mémin·Sébastien Moskowitz
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Abstract

We study a stochastic Navier--Stokes system in which the spatial modes of the transport noise evolve dynamically and are coupled to the resolved velocity. The model couples a Navier--Stokes stochastic PDE to an infinite family of linearized Navier-Stokes equations for the noise correlation modes. These latter equations may contain a hyperviscosity. We prove existence of martingale solutions in two dimensions for hyperviscosity exponent $s\geq1$, and pathwise uniqueness for $s>1$ under additional regularity of the initial noise modes. In three dimensions, we establish existence of martingale solutions for $s>3/2$. The proof combines Galerkin approximations and compactness with estimates adapted to the coupled drift and stochastic terms.

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Arnaud Debussche, Etienne Mémin, Sébastien Moskowitz. 2026-09-21. Well-posedness of a stochastic Navier-Stokes system with dynamically coupled subgrid scales. https://arxiv.org/abs/2609.24396

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