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Math 716, Mathematical Fluid Dynamics II Michael Siegel 515B Cullimore Hall 596-5835 misieg@oak.njit.edu 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 fluids. 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: 038740399X 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