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Fourier analysis and its applications to PDEs (Summer Semester 2019)

This lecture (3SWS lecture+1SWS problem class) will last only for half the summer semester (i.e. from 23.04.2019 to 07.06.2019) and correspondingly the credit points (ECTS) will only be 2. The oral exam will take place on Tuesday 11.06.2019 and please send me email for the registration at latest 04.06.2019 if you would like to take the oral exam.

Here is the timetable for the lectures and the problem classes:

23.04.2019, 29.04.2019, 06.05.2019, 07.05.2019, 13.05.2019, 20.05.2019, 21.05.2019, 27.05.2019, 03.06.2019, 04.06.2019.

Problem classes
30.04.2019, 14.05.2019, 28.05.2019.

Lecture: Monday 14:00-15:30 SR 2.59 Begin: 23.4.2019
Tuesday 15:45-17:15 (every 2nd week) SR 2.66
Problem class: Tuesday 15:45-17:15 (every 2nd week) SR 2.66 Begin: 30.4.2019
Lecturer JProf. Dr. Xian Liao
Office hours: Monday, 12:00 - 13:00.
Room 3.027 Kollegiengebäude Mathematik (20.30)
Email: xian.liao@kit.edu
Problem classes M.Sc. Zihui He
Office hours: by appointment
Room 3.030 Kollegiengebäude Mathematik (20.30)
Email: zihui.he@kit.edu

We are going to introduce the Fourier analysis theory and then to apply it to the study of various partial differential equations.

The Fourier analysis theory will include the following concepts:
-Fourier transform and Schwartz space, tempered distribution space
-Bernstein's inequality
-Littlewood-Paley decomposition
-Besov spaces and Sobolev spaces
-Paradifferential calculus

The following types of partial differential equations will be discussed:
-Transport equations
-Navier-Stokes equations

Basic concepts from functional analysis and real analysis, e.g. Lebesgue spaces, Hölder's inequality, Young's inequality, convolution.

Lecture Notes:
Lecture Notes, version 04.06.2019
Exercise sheets:
Exercise sheet 1, to be explained on 30.04.2019
Exercise sheet 2, to be explained on 14.05.2019
Exercise sheet 3, to be explained on 28.05.2019


Oral exam on 11.06.2019.


H. Bahouri, J.-Y. Chemin and R. Danchin: Fourier analysis and nonlinear partial differential equations. Springer, 2011.