Michael Siegel

Math 716, Mathematical Fluid Dynamics II
Michael Siegel
515B Cullimore Hall
Office Hours: M, W, F 1-2 or by appointment
Course Description: Further development of the ideas of fluid dynamics, with an
emphasis on mathematical developments and issues. A selection of topics will be
developed in some detail, for example: Stokes flow and low-Reynolds-number
hydrodynamics; flow at high Reynolds number and boundary layers; shock waves and
hyperbolic systems; dynamics of interfacial flows; hydrodynamic stability; rotating
Textbooks: 1. Viscous Flow, H. Ockendon and J. R. Ockendon, Cambridge University
Press. ISBN: 0521458811
2. Waves and Compressible Flow, H. Ockendon and J. R. Ockendon, Springer. ISBN:
Other useful References:
1. A Mathematical Introduction to Fluid Mechanics, A. J. Chorin and J. E.
Marsden, Third Edition, Springer Verlag.
2. Elementary Fluid Dynamics, D. J. Acheson, Oxford University Press.
3. Fluid Mechanics, L. D. Landau and E. M. Lifschitz, Pergamon Press.
Grading: 5 to 6 HW assignments 30%, Midterm 30%, Final 40%
A tentative course outline for Math 716 is provided below:
Week 1: Introduction to viscous flow, Stokes equations
Week 2: Stokes paradox, complex variable solution of biharmonic equation
Weeks 3-4: Interfacial problems, stress boundary conditions, Hele-Shaw flow
Week 5: Thin films, lubrication theory
Week 6: Boundary Layers: Prandtl’s equations, boundary layers on a flat plate
Week 7: Midterm examination. Boundary Layer’s (continued): Rotating flows controlled
by boundary layers, boundary layer separation
Week 8: Gas flow in one dimension, hyperbolic equations
Week 9: Theory of hyperbolic equations: Characteristics and Shocks, Weak solutions
Week 10: Theory of hyperbolic equations (continued): The Riemann Problem
Week 11: Combustion waves
Week 12: Stability Theory: Linear theory, thermal instability
Week 13: Centrifugal instability, instability of parallel shear flow
Week 14: Theorems on stability of viscous flow
Week 15: Final examination