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 (4)

• Mathematics and Turbulence: where do we stand?
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• On the vanishing viscosity limit in a disk
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• Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit
• The inviscid limit of Navier-Stokes for analytic data on the half-space
• A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations
• Vorticity measures and the inviscid limit
• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Weak stablity and closure in turbulence
• Boundary Vorticity Estimates for Navier-Stokes and Application to the Inviscid Limit
• On the conservation of energy in two-dimensional incompressible flows
• Energy balance for forced two-dimensional incompressible ideal fluid flow
• Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains