Potential operators, analyticity and bounded holomorphic functional calculus for the Stokes operator

This is part of a meeting of the North British Functional Aanlysis Seminar.  There will be a tea break (15:30-16:00)

In a first talk, I shall recall the basic definitions and properties of ${\mathcal{H}}^\infty}$ functional calculus. I shall show how a second order problem can be reduced to a first order system and how to construct potential operators.
In a second talk, we will see how to use potential operators for the specific problem of the Stokes operator with the so-called “natural” boundary conditions in non smooth domains.
Most parts which will be presented are taken from a joint work with Alan McIntosh (to be published soon in the journal "Revista Matematica Iberoamericana”)