*Submitted Paper*

**Inserted:** 27 apr 2022

**Last Updated:** 3 may 2022

**Year:** 2022

**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 $L^1_{\rm loc}([0,+\infty);L^{\exp}(\mathbb R^d;\mathbb R^{d\times d}))$, 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.

**Keywords:**
Orlicz spaces, Euler equations, weak-strong uniqueness, inviscid limit

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