Profile decompositions and applications to Navier-Stokes

Profile decompositions and applications to Navier-Stokes

Thu, 20/05/2010
12:30 		Gabriel Koch (OxPDE, University of Oxford) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
Profile decompositions and applications to Navier-Stokes
In this talk, we describe new profile decompositions for bounded sequences in Banach spaces of functions defined on $ \mathbb{R}^d $. In particular, for "critical spaces" of initial data for the Navier-Stokes equations, we show how these can give rise to new proofs of recent regularity theorems such as those found in the works of Escauriaza-Seregin-Sverak and Rusin-Sverak. We give an update on the state of the former and a new proof plus new results in the spirit of the latter. The new profile decompositions are constructed using wavelet theory following a method of Jaffard.