Parabolic differential equations with rough data
Herbert Koch (Bonn)
It is an important insight from harmonic analysis that maximal
functions, square functions and
Carleson measures are useful objects to understand and describe
properties of functions,
operators and differential equations. I report on joint work with Tobias
Lamm on applications of
these concepts to nonlinear parabolic equations. Instances are:
1) Wellposedness for the Navier-Stokes equations for initial data whose
components are the divergence
of BMO vector fields.
2) The solution of the Kato square root conjecture.
3) The harmonic map heat flow with initial data in BMO by Auscher et al.
4) Lipschitz perturbations to linear fronts for porous media and thin
films.