PDE Seminar The generalized Proudman-Johnson equation revisited

2009-11-02 16:30 - 2009-11-02 17:30
Faculty of Science Building 3, 2nd floor, Room 202
Marcus Wunsch (RIMS, Kyoto University)
We demonstrate the existence of solutions to the inviscid generalizedProudman-Johnson equation for parameters $a$ lying in the open interval$(-5,-1)$ which develop singularities in finite time; moreover, we showthat there are solutions which exist for all times if $a=-1$. By analyzinggeometric properties preserved by the flow, a novel blow-up criterion forsolutions arising from a special class of initial data is given.