Mathematical fluid dynamics

Additional Info

  • ECTS credits: 6
  • Semester: 1
  • University: University of L'Aquila
  • Prerequisites:

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

  • Objectives:

    This course is designed to give an overview of fluid dynamics from a mathematical viewpoint and to introduce students to  the mathematical modeling of fluid dynamic type. 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 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.

    Fluid dynamic modeling in various fields: biofluids, atmosphere and ocean, astrophysics.

    Existence of solutions for viscid and inviscid fluids.

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