In this talk I will present a recent work in which the strong ill-posedness of the two-dimensional Boussinesq system is proven. I will show explicit examples of initial data with vorticity and density gradient in \(L^{\infty}(\mathbb{R}^2)\) for which the horizontal density gradient has a strong norm inflation in infinitesimal time. This is a joint work with Roberta Bianchini (CNR) and Lars Eric Hientzsch (Bielefeld University).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006