SAAL, Juergen:COE Researcher,Analysis,Fiscal Year 2003

Partial differential equations, Functional calculus, Parabolic equations and systems, Stokes and Navier-Stokes equations, Groups and semigroups of linear operators
Research Interest:
Stokes and Navier-Stokes equations, Semigroup Theory, Maximal Regularity, Bounded H^\infty-Calculus for Linear Operators
Research Activities:
In my research I am mainly interested in PDEs of parabolic type,in particular in the Navier-Stokes equations. For the investigation of this nonlinear problem it turned out that the funtional analytic properties of the associated linear Stokes operator play an important role. For this reason I am also interested in abstract theory for linear operators, as semigroup theory, maximal regularity, and functional calculus. Paper-list: 1.A. Noll and J. Saal, H^\infty-calculus for the Stokes operator on L^q-spaces, Math. Z. 244 (2003), 651-688. 2. J. Saal, Robin Boundary Conditions and Bounded H^\infty-Calculus for the Stokes Operator, Ph.D. Thesis TU Darmstadt, Logos Verlag Berlin (2003). 3. J. Saal, Stokes and Navier-Stokes equations with Robin boundary conditions in a half-space, in preparation. 4. J. Saal, The Stokes operator with Robin boundary condition in L^1_\sigma({\mathbb R}^n_+) and L^\infty_\sigma({\mathbb R}^n_+), in preparation.