21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

J. Saal : COE Lecture Series

H - calculus for the Stokes operator on Lq - spaces

After introducing the notion and the significance of a bounded H-calculus for linear operators we will prove that the Stokes operator on Lqσ(Ω) admits this property.

Here Ω is a domain in Rn 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 Lqσ(Ω) for the mentioned domains Ω.

21st Century COE Program : Mathematics of Nonlinear Structure via Singularity