Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Mathematical Methods in Mechanics of Compressible Fluids - NMMO536

Title:	Matematické metody v mechanice stlačitelných tekutin
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. prof. RNDr. Eduard Feireisl, DrSc.
Class:	M Mgr. MA M Mgr. MA > Povinně volitelné M Mgr. MOD M Mgr. MOD > Povinně volitelné M Mgr. NVM M Mgr. NVM > Volitelné
Classification:	Mathematics > Mathematical Modeling in Physics
Incompatibility :	NDIR066
Interchangeability :	NDIR066
Is interchangeable with:	NDIR066

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: T_MUUK (05.05.2015)

Foundations of mathematical theory of dynamics of viscous compressible fluids. Introduction of basic mathematical concepts -- function spaces and other tools from functional analysis. Discussion of simple models and the existence of variational solutions.

Course completion requirements

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

Oral exam, material covered during the lectures will be required.

In case of interest, contact Milan Pokorny by e-mail.

Literature -

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

L.C. Evans: Partial differential equations, Amer. Math. Soc. 2000

E. Feireisl: Dynamics of viscous compressible fluid, Oxford University Press, Oxford 2004

P.-L. Lions: Mathematical topics in fluid dynamics, II., Oxford University Press, Oxford 1998

E. Feireisl, T. Karper, M. Pokorný: Mathematical theory of compressible viscous fluids. Analysis and numerics. Advances in Mathematical Fluid Mechanics. Lecture Notes in Mathematical Fluid Mechanics. Birkhäuser/Springer, Cham, 2016.

E. Feireisl, M. Pokorný: Mathematical theory of compressible viscous fluids, https://www2.karlin.mff.cuni.cz/~pokorny/LectureNotes/Feireisl_Pokorny_Compressible.pdf

Requirements to the exam

Last update: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2018)

At the oral exam, the knowledge of the material covered at the lectures will be required. The best source of information are the Lecture Notes available on the web.

Syllabus -

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

1. Physical background.

2. Mathematical preliminaries.

3. A priori estimates.

4. Variational solutions.

5. Pressure estimates.

6. Fundamental ideas presented on the weak compactness problem.

7. Construction of approximation of solutions.

8. Limit passages -- existence of a solution.

Entry requirements -

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

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