Modul
Semigroup Theory for the Navier-Stokes Equations [M-MATH-106663]
Credits
6Recurrence
UnregelmäßigDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-113415 | Semigroup Theory for the Navier-Stokes Equations | 6 |
Competence Certificate
The module will be completed with an oral exam of about 30 minutes.
Competence Goal
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.
Prerequisites
None
Content
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
Recommendation
The following modules are strongly recommended: Functional Analysis and Classical Methods for Partial Differential Equations.
Workload
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