Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit

摘要

We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime L2 weak limit of Leray-Hopf weak solutions of the Navier-Stokes equations on any bounded domain Omega subset of Rd, d=2,3 is a weak solution of the Euler equations. This holds for both no-slip and Navier friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.