Talk
On the regularity of the Navier-Stokes equations: A well-posedness result and open questions
- Herbert Koch (Heidelberg)
Abstract
We study the incompressible Navier-Stokes equations on 
and prove existence and uniqueness of a solution u in 
with 
provided the solution v to the heat equation with the same initial data 
satisfies 
This condition on the initial data is local in space and frequency. It extends Kato's wellposedness result in 
since 
.The function space 
is closely related to BMO:
if there exists a vector field 
with 
. This is joint work with D. Tataru.
