Modul

The module will be completed with an oral exam of about 30 minutes.

After a successful participation of the course, students are familiar with essential concepts of semigroup theory, such as analytic semigroups and fractional powers of sectorial operators. They are able to apply these concepts to the Stokes operator and derive basic regularity properties of solutions to the Stokes equations. Furthermore, they can use these concepts to construct solutions to the Navier-Stokes equations in critical spaces through an iteration scheme.

None

Content from abstract semigroup theory:

• Sectorial operators
• Analytic semigroups
• Fractional powers

Content from fluid mechanics:

• Helmholtz decomposition
• Bogovskii operator
• Stokes operator
• Mapping properties of the Stokes semigroup
• Solvability of the Navier-Stokes equations in critical spaces

The following modules are strongly recommended: Functional Analysis and Classical Methods for Partial Differential Equations.

Total workload: 180 hours

Attendance: 60 h

•  lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination