IIMAS - FENOMEC
UNAM
Birkhoff normal form for nonlinear wave equations
Resumen:
Wave equations can be considered as Hamiltonian PDEs, that is,
partial differential equations that can be considered in the form of a
Hamiltonian system. Many theorems on global existence of small amplitude
solutions of nonlinear wave equations in ${\mathbb R}^n$ depend upon a
competition between the time decay of solutions and the degree of the
nonlinearity. Decay estimates are more effective when inessential nonlinear
terms are able to be removed through a well-chosen transformation. In this
talk, we construct Birkhoff normal forms transformations for the class of
wave equations which are Hamiltonian PDEs and null forms, giving a new proof
via canonical transformations of the global existence theorems for null form
wave equations of S. Klainerman and J. Shatah in space dimensions $n \geq
3$. The critical case $n = 2$ is also under consideration. These results
are work-in-progress with A. French and C.-R. Yang.
Informes: coloquiomym@gmail.com, o al 5622-3564.