Publication

Navier-Stokes equations with Navier boundary conditions and stochastic Lie transport: Well-posedness and inviscid limit

2025

Abstract

We prove the existence and uniqueness of global, probabilistically strong, PDE-strong solutions of the 2D Stochastic Navier-Stokes Equation under Navier boundary conditions with a transport and stretching noise. We emphasise that the Navier boundary conditions enable energy estimates which appear to be prohibited for the usual no-slip condition. The importance of the Stochastic Advection by Lie Transport (SALT) structure, in comparison to a purely transport Stratonovich noise, is also highlighted in these estimates. In the particular cases of the free boundary condition and a convex domain, the inviscid limit exists and is a global, probabilistically weak, PDE-weak solution of the corresponding Stochastic Euler Equation with impermeable boundary condition.

Official source

https://infoscience.epfl.ch/entities/publication/0d584f0e-1a6b-4395-9556-68f8bb98f744

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2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0d584f0e-1a6b-4395-9556-68f8bb98f744

About this result

Related concepts (32)

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.

Boundary layer

In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

Burgers' equation

Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948. For a given field and diffusion coefficient (or kinematic viscosity, as in the original fluid mechanical context) , the general form of Burgers' equation (also known as viscous Burgers' equation) in one space dimension is the dissipative system: When the diffusion term is absent (i.

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Navier-Stokes equations with Navier boundary conditions and stochastic Lie transport: Well-posedness and inviscid limit

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