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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 2014 to 2017
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:	Czech, English
Teaching methods:	full-time

Guarantor:	prof. RNDr. Eduard Feireisl, DrSc. prof. Mgr. Milan Pokorný, Ph.D., DSc.
Teacher(s):	prof. RNDr. Eduard Feireisl, DrSc. prof. Mgr. Milan Pokorný, Ph.D., DSc.
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

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Annotation -

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.

Last update: T_MUUK (05.05.2015)

Literature - Czech

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, I.,II., Oxford University Press, Oxford 1998

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

Syllabus -

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.

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