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

22 pages. Version accepted in Journal of Differential Equations

References in corpus (3)

• Sharp nonuniqueness for the Navier-Stokes equations
• Zygmund spaces, inviscid limits and uniqueness of Euler flows
• Instability and nonuniqueness for the $2d$ Euler equations in vorticity form, after M. Vishik

Cited by in corpus (1)

• Weak solutions for the Stokes system for compressible non-Newtonian fluids with unbounded divergence