Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.24396

Authors: Debussche, Arnaud, Mémin, Etienne, Moskowitz, Sébastien

Institutions: Centre National de la Recherche Scientifique, Institut Universitaire de France, Institut de recherche mathématique de Rennes, Université de Rennes, Centre Inria de l'Université de Rennes

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214028773

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