Lecturer:
Course Type:
PhD Course
Academic Year:
2015-2016
Period:
Nov. - Mar.
Duration:
60 h
Description:
1 - Introduction: Quasi-periodic solutions, small divisor problem,
- Examples of Hamiltonian and Reversible PDEs: nonlinear wave and Schrodinger equations, KdV, Hamiltonian formulation of the water waves equations.
- A Nash-Moser implicit function theorem,
- General tools: scales of Banach spaces (Sobolev, C^k, Holder, analytic), interpolation, smoothing operators,
- KAM theorem for finite dimensional systems
2 - Quasi-periodic solutions of the water waves equations
- General tools: pseudo-differential operators, composition, adjoint, commutator, Egorov theorem,
3 - Quasi-periodic solutions of nonlinear wave equations in any dimension. Bourgain's multiscale approach and extensions.
Research Group:
Location:
A-133