Course: Mathematical Theory of Convection

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Course title Mathematical Theory of Convection
Course code KMA/MTP
Organizational form of instruction Lecture
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 2
Language of instruction Czech
Status of course Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Vodák Rostislav, RNDr. Ph.D.
Course content
1. Navier-Stokes equations. 2. Function spaces and basic inequalities. 3. Compensated compactness. 4. Existence and asymptotic behavior of solutions to the Navier-Stokes equations for compressible flow. 5. Energy inequality. 6. Classical solutions for small data.

Learning activities and teaching methods
  • Attendace - 26 hours per semester
  • Preparation for the Exam - 35 hours per semester
Learning outcomes
Understand the mathematical tools of functional analysis for Navier-Stokes equations.
Application Apply the mathematical tools of functional analysis to Navier-Stokes equations.
Understanding the mathematical tools of differential and integral calculus of functions of several variables, partial differential equations and function spaces.

Assessment methods and criteria
Oral exam

Credit: active participation during seminars. Exam: the student has to understand the subject and be able to prove all theorems.
Recommended literature
  • A. Novotný, I. Straškraba. (2004). Introduction to the mathematical theory of compressible flow. Oxford: Oxford University Press.
  • E. Feireisl. (2004). Dynamics of viscous compressible fluids. Oxford: Oxford University Press.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses - Summer