Strong ill-posedness of the logarithmically regularized 2D Euler equations in the borderline Sobolev space

Hyunju Kwon
Member, School of Mathematics
October 21, 2019

The well-posedness of the incompressible Euler equations in borderline spaces has attracted much attention in recent years. To understand the behavior of solutions in these spaces, the logarithmically regularized Euler equations were introduced. In borderline Sobolev spaces, local well-posedness was proved Chae-Wu when the regularization is sufficiently strong, while strong ill-posedness of the unregularized case was established by Bourgain-Li. In this talk, I will discuss the strong ill-posedness of the remaining intermediate regime of regularization.