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

Abstract

We provide a simple proof that the Cauchy problem for the incompressible Euler equations in Rd 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.