Reduced Stokes equations and bBounded H_\infty-calculus
by
Helmut Abels
Darmstadt University of Technology

We consider the reduced Stokes equations, which can be derived from the (generalized) Stokes equations by expressing the pressure in terms of the data and the velocity. The advantage of the reduced Stokes equations is that the pressure and the divergence equation are no longer part of the system. But a non-local operator, which is called singular Green operator, enters the system instead of the pressure. Therefore the reduced Stokes equations are not a system of differential equations. But they fit well in the calculus of pseudo-differential boundary value problems.

We will discuss the structure of the reduced Stokes resolvent equations by considering them as a perturbation of the Laplace resolvent equation by a singular Green operator. Using a certain product structure of the latter operator, the resolvent of the reduced Stokes operator can be analysed precisely. Then the calculus of pseudo-differential boundary value problems can be used to construct a parametrix of the resolvent, which enables us to prove the existence of a bounded H_\infty-calculus for the reduced Stokes operator.

Date received: June 11, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-98.