Long time solutions for a Burgers-Hilbert equation

Tuesday, March 14, 2017 - 10:00
Thackeray 427
Speaker Information
Mihaela Ifrim
Postdoctoral Fellow
UC Berkeley


Special Seminar, Room Thackeray 427

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.

Research Area