On the evolution of almost-sharp fronts for the surface quasi-geostrophic equation

On the evolution of almost-sharp fronts for the surface quasi-geostrophic equation

Thu, 05/05/2011
12:30 		Jose Rodrigo (University of Warwick) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
On the evolution of almost-sharp fronts for the surface quasi-geostrophic equation
I will describe recent work with Charles Fefferman on a construction of families of analytic almost-sharp fronts for SQG. These are special solutions of SQG which have a very sharp transition in a very thin layer. One of the main difficulties of the construction is the fact that there is no formal limit for the family of equations. I will show how to overcome this difficulty, linking the result to joint work with C. Fefferman and Kevin Luli on the existence of a "spine" for almost-sharp fronts. This is a curve, defined for every time slice by a measure-theoretic construction, that describes the evolution of the almost-sharp front.