Notes
Abstract or Additional Information
Please note the special time and place. The seminar will be held in Thackeray 427.
Abstract: We consider an initial value problem for a quadratically nonlinear inviscid Burgers- Hilbert equation that models the motion of vorticity discontinuities. We will present two methods that will lead us to the existence of small, smooth solutions over cubically nonlinear time-scales.
- The first method uses a normal form transformation, which is implemented by means of a near-identity coordinate change of the independent spatial variable.
-The second method (called the \emph{modified quasilinear energy method}) constructs an energy functional that gives good cubic energy estimates for small and smooth initial data.
Both of these methods were successfully applied to a range of very challenging problems, as for example the water waves equations.
For vorticity discontinuities, this result means that there is a cubically nonlinear time-scale before the onset of lamentation.