Mathematical Fluid-Mechanics

The aim of the course is to provide an overview of the modern mathematical theory in fluid mechanics from the theory of Kato for local and global existence of Euler and Navier-Stokes equations till the analysis of some "small divisors problems" like the construction of periodic and multi periodic nonlinear waves in Euler and Water Waves equations.

The student will be aware of the energy methods to study local and global existence of Euler and Navier-Stokes equations in 2D. Moreover the student will be aware of some perturbative methods (typical of mathematical physics) to construct periodic and multi-periodic traveling waves in fluid mechanics, based on Normal Forms, KAM and Nash-Moser methods and tools from micro-local analysis.