Navier-Stokes Equations and Related Topics (PDE III)

Navier-Stokes Equations and Related Topics (PDE III)

Semester
SoSe 2023

Lecturer
Helmut Abels

Type of course (Veranstaltungsart)
Vorlesung

German title
Navier-Stokes-Gleichungen und verwandte Themen (PDG III)

Contents
The Navier-Stokes equations describe the flow of viscous and incompressible Newtonian fluids. They are a fundamental system of partial differential equations from fluid mechanics and the basis for many other models and applications. We will give an introduction to the mathematical analysis of the Navier-Stokes equations starting from the linearized Stokes equations and Navier-Stokes system in a time-independent situation. Afterwards time-dependent problems will be studied. In particular, existence of weak and strong solutions as well as regularity and uniqueness of weak solutions will be studied, which is closely related to one of the Millenium Problems of the Clay institute. In dependence on the time and interests of the audience related topics like non-Newtonian fluids, the Euler equations and related systems of partial differential equations will be discussed.

Literature
There will be lecture notes for this course. Recommended books are:

F. Boyer, Pierre Fabrie: "Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models", Springer 2013.
H. Sohr: "The Navier-Stokes equations", Birkhäuser , 2001

Further information on the literature will be available on the GRIPS page of the course.

Recommended previous knowledge
Basic knowledge in functional analysis and partial differential equations as e.g. tought in the lecture series "Functional Analysis" and "Partial Differential Equations I" at our faculty. Advantageous, but not necessary is knowledge of the content of "Partial Differential Equations II".

Time/Date
Mo., 12-14, and Wed., 8-10

Location
M103

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=60016
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: in the GRIPS course, cf. course homepage
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: Successful participation in the exercise
classes: 50% of the maximal points in the exercise sheets, presentation of one solution
For module MV (without mark, "unbenotet"): passing a short oral
examination ("Fachgespräch", 15 min.) on the content of the lecture series

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual, by appointment, re-exam: Date: individual,
by appointment
Combined exam in agreement with the lecturer in combination with, e.g.: Partial Differential
Equations I or II, oral exam: Duration: 45 minutes, Date: individual, by appointment

Modules
BV, MV, MAngAn, PHY-B-WE3, PHY-M-VE3, CS-B-Math4, CS-M-P1, CS-M-P2, CS-M-P3

ECTS
9