Growth Of Vorticity Gradient Of The Periodic Incompressible Euler Equations With External Force

The periodic incompressible Euler equations with external force is investigated.It is shown that there is a smooth solution with vorticity gradient growing exponentially.Klatos has obtained the corresponding result for the case without external force.When external force is present,with the force itself not growing,one has to estimate the velocity field more carefully to obtain the result.Euler equations with external force is similar to the inviscid Boussinesq system without heat conduction in that in both systems,the vorticity equation has a force term.Investigating the former may throw lights on how to investigate the latter.