An introduction to the mathematical theory of the NavierStokes
Code  Completion  Credits  Range  Language 

D01MTNS_EN  ZK  4  2P  English 
 Garant předmětu:
 Zdeněk Skalák
 Lecturer:
 Zdeněk Skalák
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The goal of the subject is to inform students about the basics the mathematical theory of the NavierStokes equations for the incompressible fluid. The content of the subject: The description of the NavierStokes equations, the introduction of the fundamental concepts, the definition of the fundamental function spaces, the description of the basic relations between the function spaces, the definition of the classical and weak solution, the expulsion of the pressure from the definition of the weak solution, Helmholtz decomposition, some elementary properties of the weak solution, the proof of the existence of the weak solutions by the Galerkin method in a general domain, the discussion of several different definitions of the weak solution, qualitative properties of the weak solution, energy inequality, strong energy inequality, the sufficient conditions for the energy equality, the problem of the uniqueness and regularity, the fundamental uniqueness theorem, the role of the initial conditions, brief discussion of the asymptotic behavior of the solution, brief discussion of large solutions, brief discussion of various proofs of the existence of the weak solution, mild solutions.
 Requirements:
 Syllabus of lectures:
 Syllabus of tutorials:
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 Note:
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: