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Course, academic year 2019/2020
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Mathematical Methods in Mechanics of Compressible Fluids - NMMO536
Title in English: Matematické metody v mechanice stlačitelných tekutin
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Guarantor: doc. Mgr. Milan Pokorný, Ph.D.
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
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: doc. Mgr. Milan Pokorný, Ph.D. (07.02.2018)

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

Literature -
Last update: doc. Mgr. Milan Pokorný, Ph.D. (07.02.2018)

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, http://www.karlin.mff.cuni.cz/~pokorny/Feireisl_Pokorny_Compressible.pdf

Requirements to the exam
Last update: doc. Mgr. Milan Pokorný, Ph.D. (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: Mgr. Dalibor Šmíd, Ph.D. (05.05.2015)

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.

 
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