Mathematical analysis of viscous boundary layers
David Gérard-Varet
Université Paris-Cité
Abstract:
We will review some mathematical aspects of boundary layer theory, in the context of Navier-Stokes type equations. We will pay special attention to stability issues for two types of flows with boundary layers: classical high Reynolds number flows, and rotating flows (relevant to geophysics).
Topics to be covered include: D'Alembert's paradox, vanishing viscosity limit, Prandtl boundary layer theory, Ekman layers.
Perturbative methods and small divisors problems in fluid mechanics
Riccardo Montalto
Università di Milano
Abstract:
In this course I shall present some recent results concerning the construction of periodic and multi-periodic waves for the equations of fluid mechanics, such as the Euler and Navier-Stokes equations. The main topics I shall focus on are: Nash-Moser schemes, spectral problems for linearized equations with small divisors, vanishing viscosity limit and singular perturbation problems.
