Introduction to Dispersive Equations
Fourier
transform; Interpolation of operators and Sobolev spaces; Regularization properties of solutions to the linear problem; Nonlinear 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.
* Standard program. The teacher has the autonomy to make any changes