Infinite-energy 2D statistical solutions to the equations of incompressible fluids

Abstract

We develop the concept of an infinite-energy statistical solution to the Navier-Stokes and Euler equations in the whole plane. We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity, which includes the important special case of vortex patch initial data. Our approach is to use well-studied properties of statistical solutions in a ball of radius R to construct, in the limit as R goes to infinity, an infinite-energy solution to the Navier-Stokes equations. We then construct an infinite-energy statistical solution to the Euler equations by making a vanishing viscosity argument.

References in corpus (2)

• Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${\mathbb{R}}^2$
• Vanishing viscosity limit for an expanding domain in space

Cited by in corpus (1)

• Statistical solutions of the incompressible Euler equations