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 %$t-a.e.%$ wea...
Ausführliche Beschreibung

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. Ausführliche Beschreibung