Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces

Abstract

In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs to Lloc1([0,+∞);Lexp(Rd;Rd×d)), where Lexp denotes the Orlicz space of exponentially integrable functions. Moreover, under the same assumptions on the limit solution to the Euler system, we obtain the convergence of vanishing-viscosity Leray–Hopf weak solutions of the Navier–Stokes equations.