A strong ill-posedness result for the stably stratified Boussinesq equations
A talk in the Oberseminar Analysis series by
Lars Eric Hientzsch
| Abstract: | We consider the Boussinesq equations arising in the description of continuously stratified fluids under the influence of gravity. More precisely, we investigate a linearization of the equations characterising incompressible non-homogeneous fluids around a background density profile that increases with depth (spectrally stable density profile). We prove that the system is strongly ill-posed in the class of bounded vorticity and density gradient. The mechanism that allows us to exhibit the norm-inflation in infinitesimal time is purely nonlinear - in contrast to previous results on mild ill-posedness of the system. Time permitting, applications to the 3D axisymmetric Euler equations with small bounded initial vorticity leading to a norm-inflation of the swirl are discussed. Based on joint work with R. Bianchini (IAC Rome) and F. Iandoli (Università della Calabria). Within the CRC this talk is associated to the project(s): A1 |