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, where L exp 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.

Onsager critical solutions of the forced Navier-Stokes equations

“…x ) (this is essentially the threshold for classical "weak-strong" uniqueness results, see e.g. [19,10]). In particular uniqueness and selection both fail for solutions in L 1 ((0, T ); C α (T 3 )) for any α < 1.…”