Mathematics

Mathematical Fluid Mech

Module code: 864G1
Level 7 (Masters)
15 credits in autumn teaching
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

The aim of this module is to provide an introduction to fluid mechanics, regarded from the perspective of the mathematical analysis of underlying PDE models. As such the course is at the interface between pure and applied mathematics.

The mdoule focuses on the basic equations of fluid dynamics, namely the Navier-Stokes and Euler equations. These are the equations governing the motion of fluids, such as water or air.

The module starts with the derivation of the basic conservation laws. Some simple cases of solutions are analyzed in detail and then a general existence theory in bounded and unbounded domain is obtained, based on energy methods.

Pre-requisite

None.


Module learning outcomes

  • Understand the derivation of the basic balance laws.
  • Be able to describe simple motions predicted by the fluids, by means of some explicit solutions.
  • Understand the concept of weak solutions and their importance.
  • Understand and implement the proof of the existence of weak solutions and the role of the energy laws.