Remarks on high Reynolds numbers hydrodynamics and the inviscid limit

Abstract

We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are uniformly bounded. We also prove that $t-a.e.$ weak $L^2$ inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.

References in corpus (2)

• Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows
• On the vanishing viscosity limit in a disk