Fourier transform, operator interpolation and Sobolev spaces; Regularization properties of linear problem solutions; Non-linear Schrödinger equation, Local and global theory for the associated initial value problem; Generalized Korteweg-de Vries equation, Local and global theory for the associated initial value problem; Generalizations.

Reference:
LINARES, F., PONCE, G. – Introduction to nonlinear dispersive equations. Publicações Matemáticas, IMPA 2004.

* Basic syllabus. The teacher has the autonomy to make any changes.