COURSE CONTENTS FOR: Mathematical fluid and biofluid dynamics, Mathematical fluid dynamics, Mathematical Modelling of Continuum Media

- Derivation of the governing equations: Euler and Navier-Stokes
- Eulerian and Lagrangian description of fluid motion; examples of fluid flows
- Vorticity equation in 2D and 3D
- Dimensional analysis: Reynolds number, Mach Number, Frohde number.
- From compressible to incompressible models

COURSE CONTENTS FOR: Mathematical fluid and biofluid dynamics, Mathematical fluid dynamics

- Existence of solutions for viscid and inviscid fluids
- Fluid dynamic modeling in various fields: mixture of fluids, combustion, astrophysics, geophysical fluids (atmosphere, ocean)

COURSE CONTENTS FOR: Mathematical fluid and biofluid dynamics

- Modeling for biofluids: hemodynamics, cerebrospinal fluids, cancer modelling, animal locomotion, bioconvection for swimming microorganisms.

PREREQUISITES:

Basic notions of functional analysis, functions of complex values, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.

TEXT BOOSK:

• Franck Boyer, Pierre Fabrie- Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, Springer.
• Andrea Bertozzi, Andrew Majda- Vorticity and Incompressible Flow, Cambridge University Press.
• Roger M. Temam, Alain M. Miranville, Mathematical Modeling in Continum Mechanics, Cambridge University Press.
• Alexandre Chorin, Jerrold E. Marsden, A Mathematical Introduction to Fluid Mechanics, Springer Verlag.
• Lecture Notes

EXAM:

written exam

OFFICE HOURS:

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