L∞ Ill-Posedness for a Class of Equations Arising in Hydrodynamics

We give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of the n -dimensional Euler equations in the class C 1 ∩ L 2 ( Ω ) and also in C k ∩ L 2 ( Ω ) where Ω can be the whole space, a smooth bounded domain, or the torus. We also apply our method to the Oldroyd B, surface quasi-geostrophic, and Boussinesq systems.