Publication

The zero viscosity limit of stochastic Navier–Stokes flows

2025

Abstract

We introduce an analogue to Kato's Criterion regarding the inviscid convergence of weak solutions of the stochastic Navier–Stokes equations to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type noise models. This is achieved firstly for the typical noise scaling of [Formula presented], before considering a new parameter which approaches zero with viscosity but at a potentially different rate. We determine the implications of this for our criterion and clarify a sense in which the scaling by [Formula presented] is optimal. The criterion applies in both two and three dimensions, with some technical simplifications in the 2D case.

Official source

https://infoscience.epfl.ch/entities/publication/5ca13463-1c4c-4f36-bb35-0b2fdda40cb8

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/5ca13463-1c4c-4f36-bb35-0b2fdda40cb8

About this result

Related concepts (31)

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.

Stokes' law

In fluid dynamics, Stokes' law is an empirical law for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.

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The zero viscosity limit of stochastic Navier–Stokes flows

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