Strong Ill-Posedness in $L^{\infty }$ for the Riesz Transform Problem

Tarek M. Elgindi, Karim R. Shikh Khalil

We prove strong ill-posedness in $L^{\infty }$ for linear perturbations of the 2d Euler equations of the form: \[\partial_t ω+ u\cdot\nablaω= R(ω),\] where $R$ is any non-trivial se…