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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)
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Oral exam, material covered during the lectures will be required.
In case of interest, contact Milan Pokorny by e-mail. Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (07.02.2023)
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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 Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (07.02.2023)
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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. Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (07.02.2018)
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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)
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Basic knowlege of linear partial differential equations (Sobolev spaces, weak solution for linear elliptic, hyperbolic and parabolic PDEs) Last update: Pokorný Milan, prof. Mgr., Ph.D., DSc. (21.06.2021)
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