An alternative approach to regularity for the Navier-Stokes equations in critical spaces

An alternative approach to regularity for the Navier-Stokes equations in critical spaces

Tue, 03/11/2009
14:00 		Gabriel Koch (University of Oxford) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
An alternative approach to regularity for the Navier-Stokes equations in critical spaces
We present an alternative viewpoint on recent studies of regularity of solutions to the Navier-Stokes equations in critical spaces. In particular, we prove that mild solutions which remain bounded in the space $ \dot H^{1/2} $ do not become singular in finite time, a result which was proved in a more general setting by L. Escauriaza, G. Seregin and V. Sverak using a different approach. We use the method of "concentration-compactness" + "rigidity theorem" which was recently developed by C. Kenig and F. Merle to treat critical dispersive equations. To the authors' knowledge, this is the first instance in which this method has been applied to a parabolic equation. This is joint work with Carlos Kenig.