Calculus of Variations and Geometric Measure Theory

L. De Rosa - M. Inversi - G. Stefani

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

created by stefani on 27 Apr 2022
modified on 30 Jan 2024


Published Paper

Inserted: 27 apr 2022
Last Updated: 30 jan 2024

Journal: J. Differ. Equ.
Volume: 366
Pages: 833 - 861
Year: 2023
Doi: 10.1016/j.jde.2023.05.019

ArXiv: 2204.12779 PDF


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