Mathematical Theory of Navier-Stokes Equations - NMMO532
Title: Matematická teorie Navierových-Stokesových rovnic
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. Mgr. Milan Pokorný, Ph.D., DSc.
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
M Mgr. MOD
M Mgr. MOD > Povinně volitelné
Classification: Mathematics > Differential Equations, Potential Theory
Incompatibility : NDIR010
Interchangeability : NDIR010
Is interchangeable with: NDIR010
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Annotation -
Last update: T_MUUK (14.05.2013)
Mathematical theory regarding the existence of a weak solution and the questions of its uniqueness and regularity is presented. We focus on the evolutionary model in three spatial dimensions.
Aim of the course -
Last update: T_MUUK (14.05.2013)

To explain the students the basic notions of the theory of evolutionary Navier--Stokes equations.
Course completion requirements
Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2023)

The student is required to pass an oral exam based on the material from the lecture.

In case you are interested in the course, please contact by e-mail Milan Pokorny.

Literature -
Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2023)

G.P. Galdi: An introduction to the Navier-Stokes initial-boundary value problem, Galdi, Giovanni P. (ed.) et al., Fundamental directions in mathematical fluid mechanics, Basel: Birkhäuser, 1-70, 2000.

M. Pokorný: Navier--Stokesovy rovnice, https://www2.karlin.mff.cuni.cz/~pokorny/LectureNotes/NavierandStokes_eng.pdf

https://www2.karlin.mff.cuni.cz/~pokorny/LectureNotes/regularita_NS_English.pdf

R. Temam: Navier-Stokes equations. Theory and numerical analysis, Providence, RI: American Mathematical Society (AMS), 2001.
Teaching methods - Czech
Last update: T_MUUK (14.05.2013)

přednáška

Requirements to the exam
Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (30.04.2020)

The material covered during the lecture available also in the Lecture notes (in Czech or English for the general part and for the suitable weak solution).

Syllabus -
Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2023)

Mathematical theory regarding the existence of a weak solution and the questions of its uniqueness and regularity is presented. Suitable weak solution, partial regularity. We focus on the evolutionary model in three spatial dimensions.

Entry requirements -
Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (21.06.2021)

Basic knowledge of partial differential equations (Sobolev spaces, weak solution for linear elliptic and parabolic PDEs)