Mathematical fluid and biofluid dynamics

Additional Info

  • ECTS credits: 6
  • University: University of L'Aquila
  • Semester: 3
  • Objectives:


    The aim of the course is to give an overview of fluid dynamics from a mathematical viewpoint, and to introduce students to the mathematical modeling of fluid dynamic type with a particular attention to biofluid dynamics.

    At the end of the course students will be able to perform a qualitative and quantitative analysis of solutions for particular fluid dynamics problems and to use concepts and mathematical techniques learned from this course for the analysis of other partial differential equations.

  • Topics:


    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
    Existence of solutions for viscid and inviscid fluids
    Fluid dynamic modeling in various fields: magnetohydrodynamics, combustion, astrophysics.
    Modeling for biofluids: hemodynamics, cerebrospinal fluids, cancer modelling, animal locomotion, bioconvection for swimming microorganisms.

  • Prerequisites:


    Basic notions of functional analysis and multi variable calculus, standard properties of the heat equation, wave equation, Laplace and Poisson's equations.

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