A simple ill-posedness proof for incompressible Euler equations in critical Sobolev spaces

摘要

We provide a simple proof that the Cauchy problem for the incompressible Euler equations in R-d with any d >= 3 is ill-posed in critical Sobolev spaces, extending an earlier work of Bourgain and Li (2021) [5] in the case d = 3. The ill-posedness is shown for certain critical Lorentz spaces as well. (c) 2022 Elsevier Inc. All rights reserved.