Strong ill-posedness in $L^{\infty }$ of the 2d Boussinesq equations in vorticity form and application to the 3d axisymmetric Euler Equations

Roberta Bianchini, Lars Eric Hientzsch, Felice Iandoli

We prove the strong ill-posedness in the sense of Hadamard of the two-dimensional Boussinesq equations in $W^{1,\infty }({\mathbb{R}}^2)$ without boundary, extending to the case of s…