@article{Ciampa2024, 
author = {Gennaro Ciampa and Gianluca Crippa and Stefano Spirito},
title = {Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations},
year = {2024},
journal = {Mathematics in Engineering},
volume = {6},
number = {4},
pages = {494-509},
keywords = {incompressible Euler equations, vorticity, propagation of regularity, modulus of continuity, inviscid limit},
url = {https://www.sciopen.com/article/10.3934/mine.2024020},
doi = {10.3934/mine.2024020},
abstract = {The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with  Lp initial vorticity, provided that  p≥4. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order  |log⁡ν|−α/2 with  α>0.}
}