Zusammenfassung für den Vortrag am 14.12.1999 (15:15 Uhr)

Herbert Koch (Heidelberg)

On the regularity of the Navier-Stokes equations: A well-posedness result and open questions

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: iff there exists a vector field with . This is joint work with D. Tataru.