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Lecturer(s)
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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Functional analysis: function spaces, fixed point theorems, bifurcation, embedding theorems, compactness, dual spaces, interpolation theorems. General theory of PDE's: linear and nonlinear parabolic and elliptic equations, nonlinear hyperbolic equations of the first order, solvability of the equations. Continuum mechanics of fluids: mathematical theory of compressible and incompressible Newtonian fluids. Navier-Stokes equations: existence of solutions (stacionary and non-stacionary case), qualitative properties of the solutions, different types of flow and boundary conditions.
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Learning activities and teaching methods
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Lecture
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Learning outcomes
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Understand the mathematical tools of functional analysis to Navier-Stokes equations.
Applications. Apply the mathematical tools of functional analysis to Navier-Stokes equations.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
the student has to understand the subject
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Recommended literature
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A. Novotný, I. Straškraba. (2004). Introduction to the mathematical theory of compressible flow. Oxford: Oxford University Press.
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E. Feireisl. (2004). Dynamics of viscous compressible fluids. Oxford: Oxford University Press.
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J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
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Kufner A., John O., Fučík S. Function spaces.
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L.C. Evans. (1998). Partial differential equations. AMS.
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