## J. Saal : COE Lecture Series

### H^{∞} - calculus for the Stokes operator on L^{q} - spaces

After introducing the notion and the significance
of a bounded H^{∞}-calculus for linear operators
we will prove that the Stokes operator on
L^{q}_{σ}(Ω) admits this property.

Here Ω is a domain in **R**^{n} either bounded,
exterior, or a perturbed half-space.

The starting point will be the result on the
half-space. By using an abstract perturbation theorem,
this result can be transfered to bent half-spaces.

The application of a localizaton procedure then will
lead to the bounded H^{∞}-calculus for the Stokes
operator on L^{q}_{σ}(Ω) for the mentioned
domains Ω.